LMFDB - Embedded newform 62.6.g.b.45.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [62,6,Mod(7,62)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(62, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([28])) N = Newforms(chi, 6, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("62.7"); S:= CuspForms(chi, 6); N := Newforms(S);

Level:	$ N $	$=$	$ 62 = 2 \cdot 31 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	62.g (of order $15$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [56,56] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$9.94379682840$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$7$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			45.4
Character	$\chi$	$=$	62.45
Dual form			62.6.g.b.51.4

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.23607 + 3.80423i) q^{2} +(-0.311477 + 0.345930i) q^{3} +(-12.9443 - 9.40456i) q^{4} +(21.3689 - 37.0120i) q^{5} +(-0.930990 - 1.61252i) q^{6} +(-10.6596 + 101.419i) q^{7} +(51.7771 - 37.6183i) q^{8} +(25.3778 + 241.453i) q^{9} +(114.389 + 127.041i) q^{10} +(-518.211 + 230.722i) q^{11} +(7.28516 - 1.54851i) q^{12} +(-44.7808 - 9.51845i) q^{13} +(-372.647 - 165.913i) q^{14} +(6.14765 + 18.9205i) q^{15} +(79.1084 + 243.470i) q^{16} +(-530.921 - 236.381i) q^{17} +(-949.912 - 201.910i) q^{18} +(-1167.77 + 248.216i) q^{19} +(-624.686 + 278.128i) q^{20} +(-31.7638 - 35.2773i) q^{21} +(-237.176 - 2256.58i) q^{22} +(-1546.73 + 1123.76i) q^{23} +(-3.11408 + 29.6285i) q^{24} +(649.242 + 1124.52i) q^{25} +(91.5624 - 158.591i) q^{26} +(-182.943 - 132.916i) q^{27} +(1091.79 - 1212.55i) q^{28} +(-882.071 + 2714.74i) q^{29} -79.5768 q^{30} +(-5348.32 + 157.034i) q^{31} -1024.00 q^{32} +(81.5968 - 251.129i) q^{33} +(1555.50 - 1727.56i) q^{34} +(3525.95 + 2561.75i) q^{35} +(1942.27 - 3364.10i) q^{36} +(800.328 + 1386.21i) q^{37} +(499.167 - 4749.26i) q^{38} +(17.2409 - 12.5262i) q^{39} +(-285.908 - 2720.23i) q^{40} +(10156.5 + 11280.0i) q^{41} +(173.465 - 77.2316i) q^{42} +(12298.1 - 2614.04i) q^{43} +(8877.70 + 1887.01i) q^{44} +(9478.96 + 4220.30i) q^{45} +(-2363.19 - 7273.15i) q^{46} +(1481.36 + 4559.15i) q^{47} +(-108.864 - 48.4694i) q^{48} +(6267.44 + 1332.19i) q^{49} +(-5080.44 + 1079.88i) q^{50} +(247.141 - 110.034i) q^{51} +(490.138 + 544.353i) q^{52} +(-3923.82 - 37332.7i) q^{53} +(731.771 - 531.663i) q^{54} +(-2534.09 + 24110.3i) q^{55} +(3263.30 + 5652.20i) q^{56} +(277.866 - 481.279i) q^{57} +(-9237.17 - 6711.20i) q^{58} +(20419.8 - 22678.4i) q^{59} +(98.3623 - 302.728i) q^{60} -17662.2 q^{61} +(6013.49 - 20540.3i) q^{62} -24758.6 q^{63} +(1265.73 - 3895.53i) q^{64} +(-1309.21 + 1454.03i) q^{65} +(854.493 + 620.826i) q^{66} +(-29736.1 + 51504.5i) q^{67} +(4649.32 + 8052.87i) q^{68} +(93.0263 - 885.086i) q^{69} +(-14103.8 + 10247.0i) q^{70} +(-2131.56 - 20280.4i) q^{71} +(10397.0 + 11547.1i) q^{72} +(13120.4 - 5841.58i) q^{73} +(-6262.71 + 1331.18i) q^{74} +(-591.229 - 125.670i) q^{75} +(17450.2 + 7769.35i) q^{76} +(-17875.8 - 55016.1i) q^{77} +(26.3417 + 81.0715i) q^{78} +(19705.2 + 8773.34i) q^{79} +(10701.8 + 2274.73i) q^{80} +(-57604.2 + 12244.1i) q^{81} +(-55465.8 + 24694.9i) q^{82} +(3037.25 + 3373.21i) q^{83} +(79.3919 + 755.364i) q^{84} +(-20094.1 + 14599.2i) q^{85} +(-5256.88 + 50015.8i) q^{86} +(-664.364 - 1150.71i) q^{87} +(-18152.1 + 31440.3i) q^{88} +(-23274.6 - 16910.0i) q^{89} +(-27771.6 + 30843.5i) q^{90} +(1442.70 - 4440.18i) q^{91} +30589.8 q^{92} +(1611.55 - 1899.06i) q^{93} -19175.1 q^{94} +(-15766.9 + 48525.4i) q^{95} +(318.952 - 354.232i) q^{96} +(99907.2 + 72586.8i) q^{97} +(-12814.9 + 22196.1i) q^{98} +(-68859.7 - 119268. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 56 q^{2} - 7 q^{3} - 224 q^{4} + 91 q^{5} - 152 q^{6} - 94 q^{7} + 896 q^{8} + 896 q^{9} - 944 q^{10} - 31 q^{11} - 112 q^{12} - 1244 q^{13} + 856 q^{14} + 518 q^{15} - 3584 q^{16} + 1064 q^{17}+ \cdots - 625437 q^{99}+O(q^{100}) $ 56 * q + 56 * q^2 - 7 * q^3 - 224 * q^4 + 91 * q^5 - 152 * q^6 - 94 * q^7 + 896 * q^8 + 896 * q^9 - 944 * q^10 - 31 * q^11 - 112 * q^12 - 1244 * q^13 + 856 * q^14 + 518 * q^15 - 3584 * q^16 + 1064 * q^17 - 1724 * q^18 + 619 * q^19 - 1024 * q^20 + 9541 * q^21 + 124 * q^22 - 1717 * q^23 + 768 * q^24 - 24033 * q^25 - 1344 * q^26 + 22754 * q^27 + 1776 * q^28 + 11733 * q^29 + 13928 * q^30 + 57065 * q^31 - 57344 * q^32 - 11248 * q^33 - 10456 * q^34 - 7296 * q^35 - 42464 * q^36 - 1504 * q^37 - 29736 * q^38 - 19566 * q^39 + 4096 * q^40 + 35891 * q^41 + 40636 * q^42 + 66400 * q^43 + 23344 * q^44 - 27014 * q^45 - 7612 * q^46 + 36521 * q^47 - 3072 * q^48 + 121465 * q^49 - 13108 * q^50 - 236890 * q^51 - 19904 * q^52 - 143661 * q^53 - 91016 * q^54 + 106359 * q^55 + 5056 * q^56 + 13060 * q^57 + 59468 * q^58 + 230112 * q^59 + 8288 * q^60 - 49860 * q^61 + 26740 * q^62 + 66726 * q^63 - 57344 * q^64 + 201094 * q^65 - 30508 * q^66 + 74372 * q^67 - 4656 * q^68 - 599733 * q^69 + 29184 * q^70 + 23383 * q^71 - 27584 * q^72 - 66915 * q^73 + 186916 * q^74 + 553648 * q^75 - 152736 * q^76 + 120895 * q^77 + 142024 * q^78 - 452529 * q^79 - 50944 * q^80 - 365276 * q^81 - 14324 * q^82 - 469160 * q^83 - 50464 * q^84 - 127377 * q^85 + 215540 * q^86 + 217461 * q^87 + 39744 * q^88 - 155746 * q^89 + 820796 * q^90 - 142152 * q^91 - 5952 * q^92 + 342224 * q^93 + 29656 * q^94 + 756444 * q^95 + 7168 * q^96 + 325303 * q^97 + 533540 * q^98 - 625437 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/62\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{11}{15}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.23607	+	3.80423i	−0.218508	+	0.672499i
$2$	−1.23607	+	3.80423i	−0.218508	+	0.672499i
$3$	−0.311477	+	0.345930i	−0.0199812	+	0.0221914i	−0.753053	−	0.657960i	$-0.771419\pi$
$3$	−0.311477	+	0.345930i	−0.0199812	+	0.0221914i	0.733071	+	0.680152i	$0.238086\pi$
$4$	−12.9443	−	9.40456i	−0.404508	−	0.293893i
$5$	21.3689	−	37.0120i	0.382258	−	0.662090i	−0.609127	−	0.793073i	$-0.708480\pi$
$5$	21.3689	−	37.0120i	0.382258	−	0.662090i	0.991385	+	0.130983i	$0.0418132\pi$
$6$	−0.930990	−	1.61252i	−0.0105576	−	0.0182864i
$7$	−10.6596	+	101.419i	−0.0822236	+	0.782305i	0.873259	+	0.487257i	$0.162002\pi$
$7$	−10.6596	+	101.419i	−0.0822236	+	0.782305i	−0.955482	+	0.295048i	$0.904664\pi$
$8$	51.7771	−	37.6183i	0.286031	−	0.207813i
$9$	25.3778	+	241.453i	0.104435	+	0.993635i
$10$	114.389	+	127.041i	0.361728	+	0.401740i
$11$	−518.211	+	230.722i	−1.29129	+	0.574921i	−0.933398	−	0.358842i	$-0.883172\pi$
$11$	−518.211	+	230.722i	−1.29129	+	0.574921i	−0.357894	+	0.933762i	$0.616505\pi$
$12$	7.28516	−	1.54851i	0.0146045	−	0.00310428i
$13$	−44.7808	−	9.51845i	−0.0734908	−	0.0156210i	0.171020	−	0.985268i	$-0.445294\pi$
$13$	−44.7808	−	9.51845i	−0.0734908	−	0.0156210i	−0.244510	+	0.969647i	$0.578627\pi$
$14$	−372.647	−	165.913i	−0.508133	−	0.226235i
$15$	6.14765	+	18.9205i	0.00705474	+	0.0217122i
$16$	79.1084	+	243.470i	0.0772542	+	0.237764i
$17$	−530.921	−	236.381i	−0.445562	−	0.198377i	0.171676	−	0.985153i	$-0.445082\pi$
$17$	−530.921	−	236.381i	−0.445562	−	0.198377i	−0.617238	+	0.786777i	$0.711748\pi$
$18$	−949.912	−	201.910i	−0.691038	−	0.146885i
$19$	−1167.77	+	248.216i	−0.742116	+	0.157742i	−0.563429	−	0.826164i	$-0.690518\pi$
$19$	−1167.77	+	248.216i	−0.742116	+	0.157742i	−0.178687	+	0.983906i	$0.557185\pi$
$20$	−624.686	+	278.128i	−0.349210	+	0.155478i
$21$	−31.7638	−	35.2773i	−0.0157175	−	0.0174561i
$22$	−237.176	−	2256.58i	−0.104475	−	0.994017i
$23$	−1546.73	+	1123.76i	−0.609669	+	0.442951i	−0.849298	−	0.527914i	$-0.822974\pi$
$23$	−1546.73	+	1123.76i	−0.609669	+	0.442951i	0.239629	+	0.970865i	$0.422974\pi$
$24$	−3.11408	+	29.6285i	−0.00110357	+	0.0104998i
$25$	649.242	+	1124.52i	0.207757	+	0.359847i
$26$	91.5624	−	158.591i	0.0265634	−	0.0460092i
$27$	−182.943	−	132.916i	−0.0482954	−	0.0350887i
$28$	1091.79	−	1212.55i	0.263174	−	0.292284i
$29$	−882.071	+	2714.74i	−0.194764	+	0.599422i	0.805215	+	0.592983i	$0.202050\pi$
$29$	−882.071	+	2714.74i	−0.194764	+	0.599422i	−0.999979	+	0.00643942i	$0.997950\pi$
$30$	−79.5768			−0.0161430
$31$	−5348.32	+	157.034i	−0.999569	+	0.0293487i
$31$	−5348.32	+	157.034i	−0.999569	+	0.0293487i
$32$	−1024.00			−0.176777
$33$	81.5968	−	251.129i	0.0130433	−	0.0401432i
$34$	1555.50	−	1727.56i	0.230767	−	0.256293i
$35$	3525.95	+	2561.75i	0.486526	+	0.353482i
$36$	1942.27	−	3364.10i	0.249777	−	0.432627i
$37$	800.328	+	1386.21i	0.0961089	+	0.166466i	0.910071	−	0.414453i	$-0.136027\pi$
$37$	800.328	+	1386.21i	0.0961089	+	0.166466i	−0.813962	+	0.580918i	$0.802694\pi$
$38$	499.167	−	4749.26i	0.0560773	−	0.533540i
$39$	17.2409	−	12.5262i	0.00181509	−	0.00131874i
$40$	−285.908	−	2720.23i	−0.0282538	−	0.268817i
$41$	10156.5	+	11280.0i	0.943596	+	1.04797i	0.998774	+	0.0494930i	$0.0157605\pi$
$41$	10156.5	+	11280.0i	0.943596	+	1.04797i	−0.0551785	+	0.998477i	$0.517573\pi$
$42$	173.465	−	77.2316i	0.0151736	−	0.00675572i
$43$	12298.1	−	2614.04i	1.01430	−	0.215596i	0.329367	−	0.944202i	$-0.393165\pi$
$43$	12298.1	−	2614.04i	1.01430	−	0.215596i	0.684933	+	0.728606i	$0.259831\pi$
$44$	8877.70	+	1887.01i	0.691304	+	0.146941i
$45$	9478.96	+	4220.30i	0.697798	+	0.310679i
$46$	−2363.19	−	7273.15i	−0.164666	−	0.506790i
$47$	1481.36	+	4559.15i	0.0978172	+	0.301050i	0.987978	−	0.154597i	$-0.0494079\pi$
$47$	1481.36	+	4559.15i	0.0978172	+	0.301050i	−0.890160	+	0.455647i	$0.849408\pi$
$48$	−108.864	−	48.4694i	−0.00681996	−	0.00303644i
$49$	6267.44	+	1332.19i	0.372907	+	0.0792638i
$50$	−5080.44	+	1079.88i	−0.287393	+	0.0610873i
$51$	247.141	−	110.034i	0.0133051	−	0.00592383i
$52$	490.138	+	544.353i	0.0251368	+	0.0279172i
$53$	−3923.82	−	37332.7i	−0.191875	−	1.82557i	−0.490772	−	0.871288i	$-0.663285\pi$
$53$	−3923.82	−	37332.7i	−0.191875	−	1.82557i	0.298897	−	0.954285i	$-0.403381\pi$
$54$	731.771	−	531.663i	0.0341500	−	0.0248114i
$55$	−2534.09	+	24110.3i	−0.112958	+	1.07472i
$56$	3263.30	+	5652.20i	0.139055	+	0.240851i
$57$	277.866	−	481.279i	0.0113279	−	0.0196205i
$58$	−9237.17	−	6711.20i	−0.360553	−	0.261957i
$59$	20419.8	−	22678.4i	0.763696	−	0.848171i	−0.228411	−	0.973565i	$-0.573353\pi$
$59$	20419.8	−	22678.4i	0.763696	−	0.848171i	0.992107	+	0.125394i	$0.0400195\pi$
$60$	98.3623	−	302.728i	0.00352737	−	0.0108561i
$61$	−17662.2			−0.607742			−0.303871	−	0.952713i	$-0.598279\pi$
$61$	−17662.2			−0.607742			−0.303871	+	0.952713i	$0.598279\pi$
$62$	6013.49	−	20540.3i	0.198677	−	0.678622i
$63$	−24758.6			−0.785913
$64$	1265.73	−	3895.53i	0.0386271	−	0.118882i
$65$	−1309.21	+	1454.03i	−0.0384350	+	0.0426863i
$66$	854.493	+	620.826i	0.0241462	+	0.0175432i
$67$	−29736.1	+	51504.5i	−0.809277	+	1.40171i	0.104088	+	0.994568i	$0.466808\pi$
$67$	−29736.1	+	51504.5i	−0.809277	+	1.40171i	−0.913365	+	0.407141i	$0.866526\pi$
$68$	4649.32	+	8052.87i	0.121932	+	0.211192i
$69$	93.0263	−	885.086i	0.00235225	−	0.0223801i
$70$	−14103.8	+	10247.0i	−0.344026	+	0.249950i
$71$	−2131.56	−	20280.4i	−0.0501824	−	0.477454i	−0.990536	−	0.137255i	$-0.956172\pi$
$71$	−2131.56	−	20280.4i	−0.0501824	−	0.477454i	0.940353	−	0.340199i	$-0.110495\pi$
$72$	10397.0	+	11547.1i	0.236362	+	0.262507i
$73$	13120.4	−	5841.58i	0.288164	−	0.128299i	−0.257564	−	0.966261i	$-0.582920\pi$
$73$	13120.4	−	5841.58i	0.288164	−	0.128299i	0.545728	+	0.837962i	$0.316253\pi$
$74$	−6262.71	+	1331.18i	−0.132948	+	0.0282591i
$75$	−591.229	−	125.670i	−0.0121368	−	0.00257975i
$76$	17450.2	+	7769.35i	0.346551	+	0.154295i
$77$	−17875.8	−	55016.1i	−0.343589	−	1.05746i
$78$	26.3417	+	81.0715i	0.000490239	+	0.00150880i
$79$	19705.2	+	8773.34i	0.355234	+	0.158160i	0.576592	−	0.817032i	$-0.304382\pi$
$79$	19705.2	+	8773.34i	0.355234	+	0.158160i	−0.221358	+	0.975193i	$0.571049\pi$
$80$	10701.8	+	2274.73i	0.186952	+	0.0397380i
$81$	−57604.2	+	12244.1i	−0.975532	+	0.207356i
$82$	−55465.8	+	24694.9i	−0.910941	+	0.405577i
$83$	3037.25	+	3373.21i	0.0483933	+	0.0537462i	0.766855	−	0.641820i	$-0.221820\pi$
$83$	3037.25	+	3373.21i	0.0483933	+	0.0537462i	−0.718462	+	0.695566i	$0.755154\pi$
$84$	79.3919	+	755.364i	0.00122766	+	0.0116804i
$85$	−20094.1	+	14599.2i	−0.301663	+	0.219171i
$86$	−5256.88	+	50015.8i	−0.0766446	+	0.729225i
$87$	−664.364	−	1150.71i	−0.00941040	−	0.0162993i
$88$	−18152.1	+	31440.3i	−0.249873	+	0.432793i
$89$	−23274.6	−	16910.0i	−0.311463	−	0.226291i	0.421061	−	0.907032i	$-0.361658\pi$
$89$	−23274.6	−	16910.0i	−0.311463	−	0.226291i	−0.732524	+	0.680741i	$0.761658\pi$
$90$	−27771.6	+	30843.5i	−0.361406	+	0.401382i
$91$	1442.70	−	4440.18i	0.0182630	−	0.0562079i
$92$	30589.8			0.376796
$93$	1611.55	−	1899.06i	0.0193213	−	0.0227683i
$94$	−19175.1			−0.223830
$95$	−15766.9	+	48525.4i	−0.179241	+	0.551646i
$96$	318.952	−	354.232i	0.00353222	−	0.00392293i
$97$	99907.2	+	72586.8i	1.07812	+	0.783300i	0.977354	−	0.211610i	$-0.0678706\pi$
$97$	99907.2	+	72586.8i	1.07812	+	0.783300i	0.100766	+	0.994910i	$0.467871\pi$
$98$	−12814.9	+	22196.1i	−0.134788	+	0.233459i
$99$	−68859.7	−	119268.i	−0.706118	−	1.22303i
$100$	2171.66	−	20661.9i	0.0217166	−	0.206619i
$101$	84166.3	−	61150.4i	0.820985	−	0.596480i	−0.0960098	−	0.995380i	$-0.530608\pi$
$101$	84166.3	−	61150.4i	0.820985	−	0.596480i	0.916994	+	0.398900i	$0.130608\pi$
$102$	113.112	+	1076.19i	0.00107649	+	0.0102421i
$103$	43332.7	+	48125.8i	0.402460	+	0.446977i	0.909973	−	0.414667i	$-0.136102\pi$
$103$	43332.7	+	48125.8i	0.402460	+	0.446977i	−0.507513	+	0.861644i	$0.669435\pi$
$104$	−2676.69	+	1191.74i	−0.0242669	+	0.0108043i
$105$	−1984.44	+	421.806i	−0.0175657	+	0.00373370i
$106$	146872.	+	31218.6i	1.26962	+	0.269866i
$107$	−139355.	−	62044.7i	−1.17669	−	0.523896i	−0.277189	−	0.960815i	$-0.589403\pi$
$107$	−139355.	−	62044.7i	−1.17669	−	0.523896i	−0.899501	+	0.436920i	$0.856069\pi$
$108$	1118.05	+	3440.99i	0.00922360	+	0.0283873i
$109$	−46977.9	−	144583.i	−0.378728	−	1.16560i	−0.940929	−	0.338603i	$-0.890046\pi$
$109$	−46977.9	−	144583.i	−0.378728	−	1.16560i	0.562202	−	0.827000i	$-0.309954\pi$
$110$	−88588.6	−	39442.2i	−0.698066	−	0.310799i
$111$	−728.815	−	154.914i	−0.00561448	−	0.00119340i
$112$	−25535.9	+	5427.83i	−0.192356	+	0.0408866i
$113$	145161.	−	64629.9i	1.06943	−	0.476143i	0.204934	−	0.978776i	$-0.434302\pi$
$113$	145161.	−	64629.9i	1.06943	−	0.476143i	0.864500	+	0.502633i	$0.167635\pi$
$114$	1487.43	+	1651.96i	0.0107195	+	0.0119052i
$115$	8540.88	+	81261.0i	0.0602224	+	0.572978i
$116$	36948.7	−	26844.8i	0.254949	−	0.185232i
$117$	1161.82	−	11054.0i	0.00784650	−	0.0746545i
$118$	61033.7	+	105714.i	0.403520	+	0.698917i
$119$	29633.1	−	51326.0i	0.191827	−	0.332254i
$120$	1030.06	+	748.385i	0.00652997	+	0.00474430i
$121$	107545.	−	119441.i	0.667772	−	0.741636i
$122$	21831.6	−	67190.9i	0.132797	−	0.408706i
$123$	−7065.61			−0.0421102
$124$	70706.9	+	48265.9i	0.412960	+	0.281894i
$125$	189050.			1.08218
$126$	30603.3	−	94187.3i	0.171728	−	0.528525i
$127$	−157767.	+	175218.i	−0.867973	+	0.963981i	−0.999627	−	0.0273142i	$-0.991305\pi$
$127$	−157767.	+	175218.i	−0.867973	+	0.963981i	0.131654	+	0.991296i	$0.457971\pi$
$128$	13254.9	+	9630.27i	0.0715077	+	0.0519534i
$129$	−2926.29	+	5068.49i	−0.0154826	+	0.0268166i
$130$	−3913.17	−	6777.81i	−0.0203082	−	0.0351748i
$131$	−2885.65	+	27455.1i	−0.0146915	+	0.139780i	−0.999409	−	0.0343800i	$-0.989054\pi$
$131$	−2885.65	+	27455.1i	−0.0146915	+	0.139780i	0.984717	+	0.174160i	$0.0557210\pi$
$132$	−3417.97	+	2483.30i	−0.0170739	+	0.0124049i
$133$	−12726.0	−	121080.i	−0.0623826	−	0.593531i
$134$	−159179.	−	176786.i	−0.765814	−	0.850522i
$135$	−8828.75	+	3930.81i	−0.0416932	+	0.0185630i
$136$	−36381.8	+	7733.19i	−0.168670	+	0.0358518i
$137$	57103.0	+	12137.6i	0.259931	+	0.0552500i	0.336034	−	0.941850i	$-0.390914\pi$
$137$	57103.0	+	12137.6i	0.259931	+	0.0552500i	−0.0761029	+	0.997100i	$0.524248\pi$
$138$	3252.08	+	1447.92i	0.0145366	+	0.00647212i
$139$	67657.6	+	208229.i	0.297016	+	0.914121i	0.982537	+	0.186068i	$0.0595744\pi$
$139$	67657.6	+	208229.i	0.297016	+	0.914121i	−0.685521	+	0.728053i	$0.740426\pi$
$140$	−21548.7	−	66320.1i	−0.0929182	−	0.285973i
$141$	−2038.56	−	907.623i	−0.00863525	−	0.00384466i
$142$	79786.1	+	16959.1i	0.332052	+	0.0705799i
$143$	25402.0	−	5399.36i	0.103879	−	0.0220802i
$144$	−56779.2	+	25279.7i	−0.228183	+	0.101593i
$145$	81628.9	+	90658.1i	0.322422	+	0.358085i
$146$	6004.98	+	57133.6i	0.0233147	+	0.221824i
$147$	−2413.01	+	1753.15i	−0.00921012	+	0.00669154i
$148$	2677.03	−	25470.2i	0.0100461	−	0.0955824i
$149$	13193.9	+	22852.6i	0.0486866	+	0.0843276i	0.889342	−	0.457243i	$-0.151163\pi$
$149$	13193.9	+	22852.6i	0.0486866	+	0.0843276i	−0.840655	+	0.541571i	$0.817830\pi$
$150$	1208.88	−	2093.83i	0.00438686	−	0.00759826i
$151$	325917.	+	236793.i	1.16323	+	0.845135i	0.990183	−	0.139778i	$-0.0446390\pi$
$151$	325917.	+	236793.i	1.16323	+	0.845135i	0.173046	+	0.984914i	$0.444639\pi$
$152$	−51126.0	+	56781.2i	−0.179487	+	0.199341i
$153$	43601.5	−	134191.i	0.150582	−	0.463443i
$154$	231389.			0.786215
$155$	−108475.	+	201307.i	−0.362662	+	0.673024i
$156$	−340.975			−0.00112179
$157$	−80982.9	+	249240.i	−0.262207	+	0.806990i	0.730117	+	0.683322i	$0.239466\pi$
$157$	−80982.9	+	249240.i	−0.262207	+	0.806990i	−0.992324	+	0.123667i	$0.960534\pi$
$158$	−57732.8	+	64118.7i	−0.183984	+	0.204335i
$159$	14136.7	+	10270.9i	0.0443460	+	0.0322192i
$160$	−21881.7	+	37900.3i	−0.0675743	+	0.117042i
$161$	−97484.0	−	168847.i	−0.296393	−	0.513368i
$162$	24623.2	−	234274.i	0.0737151	−	0.701352i
$163$	−309201.	+	224648.i	−0.911533	+	0.662268i	−0.941402	−	0.337286i	$-0.890491\pi$
$163$	−309201.	+	224648.i	−0.911533	+	0.662268i	0.0298689	+	0.999554i	$0.490491\pi$
$164$	−25385.7	−	241529.i	−0.0737021	−	0.701228i
$165$	−7551.16	−	8386.41i	−0.0215925	−	0.0239809i
$166$	−16586.7	+	7384.87i	−0.0467185	+	0.0208004i
$167$	−363612.	+	77288.1i	−1.00890	+	0.214448i	−0.682579	−	0.730812i	$-0.739142\pi$
$167$	−363612.	+	77288.1i	−1.00890	+	0.214448i	−0.326319	+	0.945260i	$0.605808\pi$
$168$	−2971.71	−	631.656i	−0.00812331	−	0.00172666i
$169$	−337278.	−	150166.i	−0.908389	−	0.404441i
$170$	−30701.1	−	94488.3i	−0.0814763	−	0.250758i
$171$	−89567.9	−	275662.i	−0.234241	−	0.720919i
$172$	−183774.	−	81821.3i	−0.473655	−	0.210885i
$173$	−262910.	−	55883.3i	−0.667871	−	0.141960i	−0.138515	−	0.990360i	$-0.544233\pi$
$173$	−262910.	−	55883.3i	−0.667871	−	0.141960i	−0.529356	+	0.848400i	$0.677566\pi$
$174$	5198.77	−	1105.03i	0.0130175	−	0.00276695i
$175$	−120969.	+	53858.8i	−0.298592	+	0.132942i
$176$	−97168.9	−	107917.i	−0.236453	−	0.262608i
$177$	1484.87	+	14127.6i	0.00356251	+	0.0338950i
$178$	93098.2	−	67639.8i	0.220238	−	0.160012i
$179$	−51760.6	+	492469.i	−0.120744	+	1.14881i	0.751499	+	0.659734i	$0.229331\pi$
$179$	−51760.6	+	492469.i	−0.120744	+	1.14881i	−0.872244	+	0.489072i	$0.837336\pi$
$180$	−83008.1	−	143774.i	−0.190959	−	0.330750i
$181$	−54609.9	+	94587.1i	−0.123901	+	0.214603i	−0.921303	−	0.388846i	$-0.872874\pi$
$181$	−54609.9	+	94587.1i	−0.123901	+	0.214603i	0.797402	+	0.603449i	$0.206207\pi$
$182$	15108.2	+	10976.7i	0.0338091	+	0.0245637i
$183$	5501.35	−	6109.87i	0.0121434	−	0.0134867i
$184$	−37811.0	+	116370.i	−0.0823330	+	0.253395i
$185$	68408.4			0.146954
$186$	5232.45	+	8478.08i	0.0110898	+	0.0179686i
$187$	329667.			0.689401
$188$	23701.7	−	72946.4i	0.0489086	−	0.150525i
$189$	15430.3	−	17137.1i	0.0314211	−	0.0348966i
$190$	−165113.	−	119961.i	−0.331815	−	0.241078i
$191$	−64342.3	+	111444.i	−0.127618	+	0.221042i	−0.922753	−	0.385391i	$-0.874067\pi$
$191$	−64342.3	+	111444.i	−0.127618	+	0.221042i	0.795135	+	0.606432i	$0.207400\pi$
$192$	953.333	+	1651.22i	0.00186634	+	0.00323260i
$193$	−37556.3	+	357325.i	−0.0725755	+	0.690509i	0.896382	+	0.443282i	$0.146186\pi$
$193$	−37556.3	+	357325.i	−0.0725755	+	0.690509i	−0.968958	+	0.247227i	$0.920481\pi$
$194$	−399629.	+	290347.i	−0.762346	+	0.553877i
$195$	−95.2025	−	905.791i	−0.000179292	−	0.00170585i
$196$	−68598.9	−	76186.8i	−0.127549	−	0.141657i
$197$	315694.	−	140556.i	0.579563	−	0.258038i	−0.0959501	−	0.995386i	$-0.530589\pi$
$197$	315694.	−	140556.i	0.579563	−	0.258038i	0.675513	+	0.737348i	$0.263922\pi$
$198$	538840.	−	114534.i	0.976779	−	0.207621i
$199$	−486886.	−	103491.i	−0.871555	−	0.185255i	−0.249639	−	0.968339i	$-0.580312\pi$
$199$	−486886.	−	103491.i	−0.871555	−	0.185255i	−0.621916	+	0.783084i	$0.713645\pi$
$200$	75918.4	+	33801.0i	0.134206	+	0.0597524i
$201$	−8554.83	−	26329.1i	−0.0149356	−	0.0459669i
$202$	128595.	+	395774.i	0.221740	+	0.682447i
$203$	−265925.	−	118397.i	−0.452917	−	0.201652i
$204$	−4233.88	−	899.940i	−0.00712301	−	0.00151404i
$205$	634528.	−	134873.i	1.05455	−	0.224151i
$206$	−236644.	+	105361.i	−0.388532	+	0.172986i
$207$	−310589.	−	344944.i	−0.503802	−	0.559529i
$208$	−1225.07	−	11655.8i	−0.00196338	−	0.0186803i
$209$	547880.	−	398058.i	0.867600	−	0.630348i
$210$	848.258	−	8070.64i	0.00132733	−	0.0126287i
$211$	84170.9	+	145788.i	0.130154	+	0.225433i	0.923736	−	0.383031i	$-0.125120\pi$
$211$	84170.9	+	145788.i	0.130154	+	0.225433i	−0.793582	+	0.608463i	$0.791786\pi$
$212$	−300306.	+	520146.i	−0.458907	+	0.794851i
$213$	7679.54	+	5579.51i	0.0115981	+	0.00842650i
$214$	408284.	−	453445.i	0.609435	−	0.676846i
$215$	166046.	−	511036.i	0.244980	−	0.753972i
$216$	−14472.3			−0.0211059
$217$	41084.7	−	544097.i	0.0592285	−	0.784381i
$218$	608094.			0.866622
$219$	−2065.92	+	6358.26i	−0.00291074	+	0.00895835i
$220$	259549.	−	288258.i	0.361545	−	0.401536i
$221$	21525.1	+	15638.9i	0.0296459	+	0.0215390i
$222$	1490.19	−	2581.09i	0.00202937	−	0.00351496i
$223$	366340.	+	634520.i	0.493313	+	0.854443i	0.999970	−	0.00770421i	$-0.00245235\pi$
$223$	366340.	+	634520.i	0.493313	+	0.854443i	−0.506657	+	0.862148i	$0.669119\pi$
$224$	10915.4	−	103854.i	0.0145352	−	0.138293i
$225$	−255043.	+	185299.i	−0.335859	+	0.244016i
$226$	66437.7	+	632112.i	0.0865253	+	0.823234i
$227$	551871.	+	612915.i	0.710842	+	0.789470i	0.985063	−	0.172197i	$-0.0550866\pi$
$227$	551871.	+	612915.i	0.710842	+	0.789470i	−0.274221	+	0.961667i	$0.588420\pi$
$228$	−8123.00	+	3616.59i	−0.0103485	+	0.00460747i
$229$	1.11954e6	−	237966.i	1.41076	−	0.299865i	0.561338	−	0.827586i	$-0.310287\pi$
$229$	1.11954e6	−	237966.i	1.41076	−	0.299865i	0.849418	+	0.527721i	$0.176953\pi$
$230$	−319692.	−	67952.7i	−0.398486	−	0.0847007i
$231$	24599.6	+	10952.5i	0.0303318	+	0.0135046i
$232$	56452.6	+	173743.i	0.0688595	+	0.211928i
$233$	−194979.	−	600085.i	−0.235288	−	0.724141i	−0.997083	−	0.0763233i	$-0.975682\pi$
$233$	−194979.	−	600085.i	−0.235288	−	0.724141i	0.761796	−	0.647818i	$-0.224318\pi$
$234$	40615.9	+	18083.4i	0.0484905	+	0.0215894i
$235$	200398.	+	42595.9i	0.236714	+	0.0503151i
$236$	−477600.	+	101517.i	−0.558193	+	0.118648i
$237$	−9172.69	+	4083.94i	−0.0106078	+	0.00472290i
$238$	158627.	+	176173.i	0.181525	+	0.201603i
$239$	−92290.9	−	878089.i	−0.104512	−	0.994361i	−0.913584	−	0.406651i	$-0.866696\pi$
$239$	−92290.9	−	878089.i	−0.104512	−	0.994361i	0.809072	−	0.587709i	$-0.199970\pi$
$240$	−4120.26	+	2993.54i	−0.00461738	+	0.00335473i
$241$	−107584.	+	1.02359e6i	−0.119317	+	1.13523i	0.756974	+	0.653445i	$0.226677\pi$
$241$	−107584.	+	1.02359e6i	−0.119317	+	1.13523i	−0.876291	+	0.481782i	$0.839990\pi$
$242$	321448.	+	556765.i	0.352836	+	0.611129i
$243$	41181.5	−	71328.4i	0.0447390	−	0.0774902i
$244$	228624.	+	166105.i	0.245837	+	0.178611i
$245$	183235.	−	203503.i	0.195026	−	0.216599i
$246$	8733.57	−	26879.2i	0.00920141	−	0.0283190i
$247$	54656.1			0.0570028
$248$	−271013.	+	209325.i	−0.279808	+	0.216119i
$249$	−2112.93			−0.00215966
$250$	−233678.	+	719188.i	−0.236466	+	0.727767i
$251$	933258.	−	1.03649e6i	0.935013	−	1.03844i	−0.0641669	−	0.997939i	$-0.520439\pi$
$251$	933258.	−	1.03649e6i	0.935013	−	1.03844i	0.999180	−	0.0404977i	$-0.0128943\pi$
$252$	320482.	+	232844.i	0.317908	+	0.230974i
$253$	542254.	−	939211.i	0.532600	−	0.922490i
$254$	−471557.	−	816761.i	−0.458617	−	0.794348i
$255$	1208.54	−	11498.5i	0.00116389	−	0.0110736i
$256$	−53019.7	+	38521.1i	−0.0505636	+	0.0367366i
$257$	54213.4	+	515806.i	0.0512005	+	0.487140i	0.989834	+	0.142225i	$0.0454256\pi$
$257$	54213.4	+	515806.i	0.0512005	+	0.487140i	−0.938634	+	0.344915i	$0.887908\pi$
$258$	−15664.6	−	17397.3i	−0.0146511	−	0.0162717i
$259$	−149120.	+	66392.4i	−0.138129	+	0.0614991i
$260$	30621.3	−	6508.75i	0.0280925	−	0.00597124i
$261$	−677867.	−	144085.i	−0.615947	−	0.130924i
$262$	−100879.	−	44914.1i	−0.0907917	−	0.0404231i
$263$	185938.	+	572257.i	0.165759	+	0.510155i	0.999091	−	0.0426178i	$-0.0135698\pi$
$263$	185938.	+	572257.i	0.165759	+	0.510155i	−0.833332	+	0.552773i	$0.813570\pi$
$264$	−5222.20	−	16072.3i	−0.00461151	−	0.0141928i
$265$	−1.46560e6	−	652529.i	−1.28204	−	0.570801i
$266$	476346.	+	101251.i	0.412780	+	0.0877391i
$267$	13099.1	−	2784.31i	0.0112451	−	0.00239023i
$268$	869290.	−	387033.i	0.739311	−	0.329163i
$269$	−1.54167e6	−	1.71220e6i	−1.29901	−	1.44269i	−0.828172	−	0.560473i	$-0.810619\pi$
$269$	−1.54167e6	−	1.71220e6i	−1.29901	−	1.44269i	−0.470835	−	0.882221i	$-0.656047\pi$
$270$	−4040.77	−	38445.3i	−0.00337329	−	0.0320948i
$271$	−591132.	+	429482.i	−0.488946	+	0.355240i	−0.804779	−	0.593575i	$-0.797716\pi$
$271$	−591132.	+	429482.i	−0.488946	+	0.355240i	0.315833	+	0.948815i	$0.397716\pi$
$272$	15551.6	−	147963.i	0.0127454	−	0.121264i
$273$	1086.62	+	1882.09i	0.000882414	+	0.00152839i
$274$	−116757.	+	202230.i	−0.0939525	+	0.162731i
$275$	−595896.	−	432944.i	−0.475159	−	0.345223i
$276$	−9528.00	+	10581.9i	−0.00752886	+	0.00836165i
$277$	−322871.	+	993695.i	−0.252831	+	0.778133i	0.741419	+	0.671043i	$0.234153\pi$
$277$	−322871.	+	993695.i	−0.252831	+	0.778133i	−0.994249	+	0.107090i	$0.965847\pi$
$278$	−875778.			−0.679645
$279$	−173645.	−	1.28738e6i	−0.133552	−	0.990142i
$280$	278932.			0.212620
$281$	−234679.	+	722269.i	−0.177300	+	0.545674i	−0.999731	−	0.0231912i	$-0.992617\pi$
$281$	−234679.	+	722269.i	−0.177300	+	0.545674i	0.822431	+	0.568865i	$0.192617\pi$
$282$	5972.60	−	6633.24i	0.00447240	−	0.00496710i
$283$	714839.	+	519361.i	0.530569	+	0.385481i	0.820571	−	0.571545i	$-0.193656\pi$
$283$	714839.	+	519361.i	0.530569	+	0.385481i	−0.290001	+	0.957026i	$0.593656\pi$
$284$	−163137.	+	282562.i	−0.120021	+	0.207882i
$285$	−11875.4	−	20568.8i	−0.00866035	−	0.0150002i
$286$	−10858.2	+	103309.i	−0.00784952	+	0.0746832i
$287$	−1.25227e6	+	909831.i	−0.897418	+	0.652012i
$288$	−25986.8	−	247248.i	−0.0184617	−	0.175652i
$289$	−724069.	−	804160.i	−0.509959	−	0.566367i
$290$	−445783.	+	198475.i	−0.311264	+	0.138583i
$291$	−56228.7	+	11951.8i	−0.0389247	+	0.00827371i
$292$	−224772.	−	47776.7i	−0.154271	−	0.0327913i
$293$	2.45484e6	+	1.09296e6i	1.67053	+	0.743766i	0.999998	+	0.00188238i	$0.000599182\pi$
$293$	2.45484e6	+	1.09296e6i	1.67053	+	0.743766i	0.670528	+	0.741884i	$0.266067\pi$
$294$	−3686.75	−	11346.6i	−0.00248757	−	0.00765595i
$295$	−403027.	−	1.24039e6i	−0.269637	−	0.829856i
$296$	93585.4	+	41666.9i	0.0620839	+	0.0276415i
$297$	125469.	+	26669.4i	0.0825367	+	0.0175437i
$298$	−103245.	+	21945.4i	−0.0673486	+	0.0143154i
$299$	79960.1	−	35600.6i	0.0517244	−	0.0230292i
$300$	6471.16	+	7186.96i	0.00415125	+	0.00461043i
$301$	134022.	+	1.27513e6i	0.0852626	+	0.811219i
$302$	−1.30367e6	+	947172.i	−0.822527	+	0.597601i
$303$	−5062.09	+	48162.6i	−0.00316755	+	0.0301372i
$304$	−152813.	−	264680.i	−0.0948369	−	0.164262i
$305$	−377421.	+	653712.i	−0.232314	+	0.402380i
$306$	456600.	+	331740.i	0.278761	+	0.202532i
$307$	−343504.	+	381500.i	−0.208011	+	0.231020i	−0.838118	−	0.545488i	$-0.816344\pi$
$307$	−343504.	+	381500.i	−0.208011	+	0.231020i	0.630107	+	0.776508i	$0.283011\pi$
$308$	−286013.	+	880257.i	−0.171794	+	0.528729i
$309$	−30145.3			−0.0179607
$310$	−631736.	−	661495.i	−0.373363	−	0.390951i
$311$	1.60905e6			0.943339			0.471670	−	0.881775i	$-0.343651\pi$
$311$	1.60905e6			0.943339			0.471670	+	0.881775i	$0.343651\pi$
$312$	421.468	−	1297.14i	0.000245119	−	0.000754400i
$313$	−1.04544e6	+	1.16108e6i	−0.603167	+	0.669884i	−0.964967	−	0.262371i	$-0.915495\pi$
$313$	−1.04544e6	+	1.16108e6i	−0.603167	+	0.669884i	0.361800	+	0.932256i	$0.382162\pi$
$314$	−848064.	−	616154.i	−0.485405	−	0.352667i
$315$	−529063.	+	916364.i	−0.300422	+	0.520345i
$316$	−172561.	−	298884.i	−0.0972129	−	0.168378i
$317$	−270827.	+	2.57675e6i	−0.151371	+	1.44020i	0.610264	+	0.792198i	$0.291063\pi$
$317$	−270827.	+	2.57675e6i	−0.151371	+	1.44020i	−0.761636	+	0.648005i	$0.775603\pi$
$318$	−56546.7	+	41083.6i	−0.0313573	+	0.0227824i
$319$	−169251.	−	1.61032e6i	−0.0931227	−	0.886003i
$320$	−117134.	−	130090.i	−0.0639451	−	0.0710183i
$321$	64868.8	−	28881.5i	0.0351377	−	0.0156443i
$322$	762830.	−	162144.i	0.410004	−	0.0871490i
$323$	678665.	+	144255.i	0.361951	+	0.0769350i
$324$	860795.	+	383251.i	0.455551	+	0.202824i
$325$	−18369.9	−	56536.7i	−0.00964712	−	0.0296908i
$326$	−472418.	−	1.45395e6i	−0.246197	−	0.757716i
$327$	64648.1	+	28783.2i	0.0334338	+	0.0148857i
$328$	950209.	+	201973.i	0.487680	+	0.103659i
$329$	−478177.	+	101640.i	−0.243556	+	0.0517695i
$330$	41237.6	−	18360.1i	0.0208453	−	0.00928092i
$331$	−1.69140e6	−	1.87849e6i	−0.848547	−	0.942407i	0.150384	−	0.988628i	$-0.451949\pi$
$331$	−1.69140e6	−	1.87849e6i	−0.848547	−	0.942407i	−0.998931	+	0.0462207i	$0.985282\pi$
$332$	−7591.44	−	72227.7i	−0.00377989	−	0.0359632i
$333$	−314394.	+	228421.i	−0.155369	+	0.112882i
$334$	155428.	−	1.47880e6i	0.0762364	−	0.725341i
$335$	1.27086e6	+	2.20119e6i	0.618706	+	1.07163i
$336$	6076.20	−	10524.3i	0.00293619	−	0.00508562i
$337$	985502.	+	716009.i	0.472697	+	0.343435i	0.798491	−	0.602006i	$-0.205632\pi$
$337$	985502.	+	716009.i	0.472697	+	0.343435i	−0.325794	+	0.945441i	$0.605632\pi$
$338$	988164.	−	1.09747e6i	0.470476	−	0.522516i
$339$	−22856.9	+	70346.3i	−0.0108023	+	0.0332462i
$340$	397403.			0.186438
$341$	2.73532e6	−	1.31535e6i	1.27386	−	0.612571i
$342$	1.15939e6			0.536000
$343$	−731557.	+	2.25150e6i	−0.335747	+	1.03332i
$344$	538424.	−	597980.i	0.245317	−	0.272452i
$345$	−30770.9	−	22356.4i	−0.0139185	−	0.0101124i
$346$	537568.	−	931095.i	0.241403	−	0.418123i
$347$	−1.64194e6	−	2.84393e6i	−0.732040	−	1.26793i	−0.956010	−	0.293334i	$-0.905235\pi$
$347$	−1.64194e6	−	2.84393e6i	−0.732040	−	1.26793i	0.223971	−	0.974596i	$-0.428098\pi$
$348$	−2222.24	+	21143.2i	−0.000983655	+	0.00935885i
$349$	−800136.	+	581333.i	−0.351642	+	0.255483i	−0.749557	−	0.661939i	$-0.769734\pi$
$349$	−800136.	+	581333.i	−0.351642	+	0.255483i	0.397916	+	0.917422i	$0.369734\pi$
$350$	−55365.4	−	526766.i	−0.0241584	−	0.229852i
$351$	6927.16	+	7693.40i	0.00300115	+	0.00333311i
$352$	530648.	−	236260.i	0.228270	−	0.101633i
$353$	−707777.	+	150443.i	−0.302315	+	0.0642590i	−0.356572	−	0.934268i	$-0.616054\pi$
$353$	−707777.	+	150443.i	−0.302315	+	0.0642590i	0.0542566	+	0.998527i	$0.482721\pi$
$354$	−55580.1	−	11813.9i	−0.0235728	−	0.00501055i
$355$	−796168.	−	354477.i	−0.335300	−	0.149285i
$356$	142241.	+	437774.i	0.0594841	+	0.183073i
$357$	8525.19	+	26237.8i	0.00354025	+	0.0108958i
$358$	−1.80949e6	−	805635.i	−0.746187	−	0.332224i
$359$	3.76487e6	+	800249.i	1.54175	+	0.327709i	0.898856	−	0.438244i	$-0.144400\pi$
$359$	3.76487e6	+	800249.i	1.54175	+	0.327709i	0.642896	+	0.765954i	$0.277733\pi$
$360$	649553.	−	138067.i	0.264155	−	0.0561479i
$361$	−959964.	+	427403.i	−0.387692	+	0.172612i
$362$	−292329.	−	324664.i	−0.117247	−	0.130216i
$363$	7820.42	+	74406.4i	0.00311504	+	0.0296376i
$364$	−60432.7	+	43906.9i	−0.0239066	+	0.0173692i
$365$	64159.8	−	610440.i	0.0252076	−	0.239834i
$366$	16443.3	+	28480.6i	0.00641632	+	0.0111134i
$367$	1.16832e6	−	2.02359e6i	0.452791	−	0.784256i	−0.545768	−	0.837937i	$-0.683762\pi$
$367$	1.16832e6	−	2.02359e6i	0.452791	−	0.784256i	0.998558	+	0.0536803i	$0.0170952\pi$
$368$	−395962.	−	287683.i	−0.152417	−	0.110738i
$369$	−2.46584e6	+	2.73859e6i	−0.942755	+	1.04703i
$370$	−84557.5	+	260241.i	−0.0321106	+	0.0988261i
$371$	3.82809e6			1.44393
$372$	−38720.2	+	9425.93i	−0.0145071	+	0.00353156i
$373$	4.11825e6			1.53264			0.766320	−	0.642459i	$-0.222086\pi$
$373$	4.11825e6			1.53264			0.766320	+	0.642459i	$0.222086\pi$
$374$	−407491.	+	1.25413e6i	−0.150640	+	0.463621i
$375$	−58884.6	+	65398.0i	−0.0216234	+	0.0240152i
$376$	248208.	+	180333.i	0.0905411	+	0.0657819i
$377$	65339.9	−	113172.i	0.0236769	−	0.0410096i
$378$	46120.5	+	79883.1i	0.0166022	+	0.0287558i
$379$	379515.	−	3.61085e6i	0.135716	−	1.29125i	−0.688608	−	0.725134i	$-0.741778\pi$
$379$	379515.	−	3.61085e6i	0.135716	−	1.29125i	0.824324	−	0.566119i	$-0.191556\pi$
$380$	660451.	−	479846.i	0.234629	−	0.170468i
$381$	−11472.4	−	109152.i	−0.00404894	−	0.0385231i
$382$	−344427.	−	382525.i	−0.120765	−	0.134123i
$383$	3.88796e6	−	1.73103e6i	1.35433	−	0.602987i	0.404153	−	0.914692i	$-0.367566\pi$
$383$	3.88796e6	−	1.73103e6i	1.35433	−	0.602987i	0.950179	+	0.311704i	$0.100900\pi$
$384$	−7460.01	+	1585.67i	−0.00258173	+	0.000548764i
$385$	−2.41824e6	−	514013.i	−0.831472	−	0.176735i
$386$	−1.31292e6	−	584550.i	−0.448508	−	0.199689i
$387$	943266.	+	2.90308e6i	0.320153	+	0.985328i
$388$	−610578.	−	1.87917e6i	−0.205903	−	0.633703i
$389$	−3.69339e6	−	1.64440e6i	−1.23752	−	0.550977i	−0.319524	−	0.947578i	$-0.603523\pi$
$389$	−3.69339e6	−	1.64440e6i	−1.23752	−	0.550977i	−0.917991	+	0.396601i	$0.870190\pi$
$390$	3563.51	+	757.448i	0.00118636	+	0.000252169i
$391$	1.08683e6	−	231012.i	0.359516	−	0.0764175i
$392$	374625.	−	166794.i	0.123135	−	0.0548232i
$393$	−8598.75	−	9549.87i	−0.00280837	−	0.00311901i
$394$	144488.	+	1.37471e6i	0.0468910	+	0.446139i
$395$	745797.	−	541854.i	0.240507	−	0.174739i
$396$	−230330.	+	2.19144e6i	−0.0738094	+	0.702249i
$397$	261768.	+	453396.i	0.0833568	+	0.144378i	0.904690	−	0.426071i	$-0.140103\pi$
$397$	261768.	+	453396.i	0.0833568	+	0.144378i	−0.821333	+	0.570449i	$0.806769\pi$
$398$	995528.	−	1.72430e6i	0.315025	−	0.545640i
$399$	45849.1	+	33311.3i	0.0144178	+	0.0104751i
$400$	−222427.	+	247030.i	−0.0695084	+	0.0771970i
$401$	−1.44839e6	+	4.45769e6i	−0.449805	+	1.38436i	0.427321	+	0.904100i	$0.359457\pi$
$401$	−1.44839e6	+	4.45769e6i	−0.449805	+	1.38436i	−0.877127	+	0.480259i	$0.840543\pi$
$402$	110736.			0.0341762
$403$	240996.	+	43875.6i	0.0739176	+	0.0134574i
$404$	−1.66457e6			−0.507396
$405$	−777756.	+	2.39369e6i	−0.235617	+	0.725154i
$406$	779111.	−	865290.i	0.234576	−	0.260523i
$407$	−734568.	−	533695.i	−0.219809	−	0.159701i
$408$	8656.94	−	14994.3i	0.00257463	−	0.00445938i
$409$	−2.38516e6	−	4.13121e6i	−0.705032	−	1.22115i	−0.966680	−	0.255987i	$-0.917599\pi$
$409$	−2.38516e6	−	4.13121e6i	−0.705032	−	1.22115i	0.261649	−	0.965163i	$-0.415734\pi$
$410$	−271232.	+	2.58060e6i	−0.0796859	+	0.758161i
$411$	−21985.0	+	15973.1i	−0.00641982	+	0.00466427i
$412$	−108308.	−	1.03048e6i	−0.0314352	−	0.299086i
$413$	2.08237e6	+	2.31271e6i	0.600735	+	0.667183i
$414$	1.69615e6	−	755176.i	0.486367	−	0.216545i
$415$	189752.	−	40333.0i	0.0540836	−	0.0114958i
$416$	45855.5	+	9746.89i	0.0129915	+	0.00276142i
$417$	−93106.3	−	41453.6i	−0.0262204	−	0.0116741i
$418$	837086.	+	2.57628e6i	0.234331	+	0.721196i
$419$	34914.4	+	107455.i	0.00971560	+	0.0299015i	0.955797	−	0.294028i	$-0.0949959\pi$
$419$	34914.4	+	107455.i	0.00971560	+	0.0299015i	−0.946081	+	0.323930i	$0.894996\pi$
$420$	29654.0	+	13202.8i	0.00820277	+	0.00365211i
$421$	−1.74819e6	−	371589.i	−0.480710	−	0.102178i	−0.0388179	−	0.999246i	$-0.512359\pi$
$421$	−1.74819e6	−	371589.i	−0.480710	−	0.102178i	−0.441892	+	0.897068i	$0.645693\pi$
$422$	−658653.	+	140001.i	−0.180043	+	0.0382692i
$423$	−1.06323e6	+	473380.i	−0.288919	+	0.128635i
$424$	−1.60755e6	−	1.78537e6i	−0.434261	−	0.482296i
$425$	−78880.8	−	750500.i	−0.0211836	−	0.201548i
$426$	−30718.2	+	22318.1i	−0.00820109	+	0.00595844i
$427$	188272.	−	1.79129e6i	0.0499707	−	0.475440i
$428$	1.22034e6	+	2.11369e6i	0.322012	+	0.557741i
$429$	−6044.33	+	10469.1i	−0.00158564	+	0.00274641i
$430$	1.73885e6	+	1.26335e6i	0.453515	+	0.329498i
$431$	3.23352e6	−	3.59119e6i	0.838460	−	0.931204i	−0.159976	−	0.987121i	$-0.551142\pi$
$431$	3.23352e6	−	3.59119e6i	0.838460	−	0.931204i	0.998435	+	0.0559171i	$0.0178082\pi$
$432$	17888.7	−	55055.9i	0.00461180	−	0.0141937i
$433$	−2.42430e6			−0.621392			−0.310696	−	0.950509i	$-0.600562\pi$
$433$	−2.42430e6			−0.621392			−0.310696	+	0.950509i	$0.600562\pi$
$434$	2.01909e6	+	828837.i	0.514553	+	0.211225i
$435$	−56786.9			−0.0143888
$436$	−751646.	+	2.31333e6i	−0.189364	+	0.582802i
$437$	1.52728e6	−	1.69622e6i	0.382573	−	0.424891i
$438$	−21634.6	−	15718.5i	−0.00538845	−	0.00391494i
$439$	−3.09681e6	+	5.36384e6i	−0.766927	+	1.32836i	0.172295	+	0.985045i	$0.444882\pi$
$439$	−3.09681e6	+	5.36384e6i	−0.766927	+	1.32836i	−0.939222	+	0.343311i	$0.888452\pi$
$440$	775779.	+	1.34369e6i	0.191032	+	0.330877i
$441$	−162607.	+	1.54710e6i	−0.0398147	+	0.378811i
$442$	−86100.3	+	62555.5i	−0.0209628	+	0.0152304i
$443$	101749.	+	968077.i	0.0246332	+	0.234369i	0.999910	+	0.0133844i	$0.00426050\pi$
$443$	101749.	+	968077.i	0.0246332	+	0.234369i	−0.975277	+	0.220985i	$0.929073\pi$
$444$	7977.08	+	8859.44i	0.00192038	+	0.00213279i
$445$	−1.12322e6	+	500091.i	−0.268884	+	0.119715i
$446$	−2.86668e6	+	609332.i	−0.682405	+	0.145050i
$447$	−12015.0	−	2553.87i	−0.00284417	−	0.000604546i
$448$	381590.	+	169895.i	0.0898260	+	0.0399931i
$449$	−859235.	−	2.64445e6i	−0.201139	−	0.619042i	−0.999850	−	0.0173272i	$-0.994484\pi$
$449$	−859235.	−	2.64445e6i	−0.201139	−	0.619042i	0.798711	−	0.601715i	$-0.205516\pi$
$450$	−389671.	−	1.19928e6i	−0.0907124	−	0.279184i
$451$	−7.86577e6	−	3.50207e6i	−1.82096	−	0.810743i
$452$	−2.48682e6	−	528590.i	−0.572530	−	0.121695i
$453$	−183429.	+	38989.1i	−0.0419975	+	0.00892685i
$454$	−3.01382e6	+	1.34184e6i	−0.686242	+	0.305535i
$455$	−133511.	−	148279.i	−0.0302335	−	0.0335777i
$456$	−3717.75	−	35372.1i	−0.000837276	−	0.00796615i
$457$	1.32076e6	−	959588.i	0.295824	−	0.214929i	−0.429966	−	0.902845i	$-0.641474\pi$
$457$	1.32076e6	−	959588.i	0.295824	−	0.214929i	0.725790	+	0.687916i	$0.241474\pi$
$458$	−478554.	+	4.55314e6i	−0.106602	+	1.01425i
$459$	65709.4	+	113812.i	0.0145578	+	0.0252148i
$460$	653669.	−	1.13219e6i	0.144033	−	0.249473i
$461$	4.82162e6	+	3.50311e6i	1.05667	+	0.767718i	0.973470	−	0.228814i	$-0.0734849\pi$
$461$	4.82162e6	+	3.50311e6i	1.05667	+	0.767718i	0.0832034	+	0.996533i	$0.473485\pi$
$462$	−72072.4	+	80044.5i	−0.0157096	+	0.0174472i
$463$	−415117.	+	1.27760e6i	−0.0899949	+	0.276976i	−0.985917	−	0.167235i	$-0.946516\pi$
$463$	−415117.	+	1.27760e6i	−0.0899949	+	0.276976i	0.895922	+	0.444211i	$0.146516\pi$
$464$	−730737.			−0.157567
$465$	−35850.7	−	100227.i	−0.00768892	−	0.0214958i
$466$	2.52387e6			0.538396
$467$	−1.57436e6	+	4.84540e6i	−0.334051	+	1.02810i	0.633136	+	0.774040i	$0.281767\pi$
$467$	−1.57436e6	+	4.84540e6i	−0.334051	+	1.02810i	−0.967187	+	0.254064i	$0.918233\pi$
$468$	−118997.	+	132160.i	−0.0251144	+	0.0278923i
$469$	−4.90658e6	−	3.56484e6i	−1.03002	−	0.748355i
$470$	−409750.	+	709708.i	−0.0855608	+	0.148196i
$471$	−60995.2	−	105647.i	−0.0126690	−	0.0219434i
$472$	204152.	−	1.94238e6i	0.0421793	−	0.401309i
$473$	−5.76988e6	+	4.19207e6i	−1.18581	+	0.861540i
$474$	−4198.18	−	39943.0i	−0.000858252	−	0.00816573i
$475$	−1.03729e6	−	1.15202e6i	−0.210943	−	0.234276i
$476$	−866277.	+	385692.i	−0.175243	+	0.0780230i
$477$	8.91452e6	−	1.89484e6i	1.79392	−	0.381308i
$478$	3.45453e6	+	734283.i	0.691543	+	0.146992i
$479$	−7.74988e6	−	3.45047e6i	−1.54332	−	0.687130i	−0.553950	−	0.832550i	$-0.686880\pi$
$479$	−7.74988e6	−	3.45047e6i	−1.54332	−	0.687130i	−0.989370	+	0.145420i	$0.953547\pi$
$480$	−6295.19	−	19374.6i	−0.00124711	−	0.00383822i
$481$	−22644.8	−	69693.4i	−0.00446277	−	0.0137350i
$482$	−3.76098e6	−	1.67450e6i	−0.737367	−	0.328297i
$483$	88773.3	+	18869.3i	0.0173147	+	0.00368035i
$484$	−2.51539e6	+	534663.i	−0.488081	+	0.103745i
$485$	4.82149e6	−	2.14666e6i	0.930736	−	0.414390i
$486$	220446.	+	244830.i	0.0423362	+	0.0470192i
$487$	−773247.	−	7.35696e6i	−0.147739	−	1.40565i	−0.777513	−	0.628867i	$-0.783519\pi$
$487$	−773247.	−	7.35696e6i	−0.147739	−	1.40565i	0.629774	−	0.776779i	$-0.283148\pi$
$488$	−914496.	+	664420.i	−0.173833	+	0.126297i
$489$	18596.6	−	176935.i	0.00351691	−	0.0334612i
$490$	547681.	+	948611.i	0.103048	+	0.178484i
$491$	2.04674e6	−	3.54505e6i	0.383141	−	0.663619i	−0.608369	−	0.793655i	$-0.708176\pi$
$491$	2.04674e6	−	3.54505e6i	0.383141	−	0.663619i	0.991509	+	0.130035i	$0.0415091\pi$
$492$	91459.2	+	66449.0i	0.0170339	+	0.0123759i
$493$	1.11002e6	−	1.23281e6i	0.205691	−	0.228443i
$494$	−67558.6	+	207924.i	−0.0124556	+	0.0383343i
$495$	−5.88582e6			−1.07968
$496$	−461330.	−	1.28973e6i	−0.0841990	−	0.235394i
$497$	2.07955e6			0.377641
$498$	2611.72	−	8038.05i	0.000471904	−	0.00145237i
$499$	4.74435e6	−	5.26914e6i	0.852954	−	0.947301i	−0.146165	−	0.989260i	$-0.546693\pi$
$499$	4.74435e6	−	5.26914e6i	0.852954	−	0.947301i	0.999119	+	0.0419589i	$0.0133599\pi$
$500$	−2.44711e6	−	1.77793e6i	−0.437753	−	0.318046i
$501$	86520.5	−	149858.i	0.0154001	−	0.0266738i
$502$	2.78947e6	+	4.83150e6i	0.494039	+	0.855701i
$503$	185726.	−	1.76707e6i	0.0327306	−	0.311411i	−0.965892	−	0.258945i	$-0.916625\pi$
$503$	185726.	−	1.76707e6i	0.0327306	−	0.311411i	0.998623	−	0.0524659i	$-0.0167081\pi$
$504$	−1.28193e6	+	931375.i	−0.224795	+	0.163323i
$505$	−464758.	−	4.42188e6i	−0.0810958	−	0.771575i
$506$	2.90271e6	+	3.22378e6i	0.503996	+	0.559744i
$507$	157001.	−	69901.5i	0.0271258	−	0.0120772i
$508$	3.69002e6	−	784338.i	0.634409	−	0.134848i
$509$	−415440.	−	88304.5i	−0.0710745	−	0.0151073i	0.172237	−	0.985056i	$-0.444900\pi$
$509$	−415440.	−	88304.5i	−0.0710745	−	0.0151073i	−0.243312	+	0.969948i	$0.578234\pi$
$510$	42249.0	+	18810.5i	0.00719268	+	0.00320239i
$511$	452591.	+	1.39293e6i	0.0766751	+	0.235982i
$512$	−81007.0	−	249314.i	−0.0136568	−	0.0420312i
$513$	246626.	+	109805.i	0.0413757	+	0.0184217i
$514$	−2.02926e6	−	431332.i	−0.338789	−	0.0720118i
$515$	2.70720e6	−	575434.i	0.449783	−	0.0956043i
$516$	85545.7	−	38087.4i	0.0141441	−	0.00629734i
$517$	−1.81955e6	−	2.02082e6i	−0.299391	−	0.332507i
$518$	−68249.5	−	649351.i	−0.0111757	−	0.106330i
$519$	101222.	−	73542.2i	0.0164952	−	0.0119845i
$520$	−13089.2	+	124536.i	−0.00212278	+	0.0201969i
$521$	6.08049e6	+	1.05317e7i	0.981396	+	1.69983i	0.656971	+	0.753915i	$0.271837\pi$
$521$	6.08049e6	+	1.05317e7i	0.981396	+	1.69983i	0.324424	+	0.945912i	$0.394829\pi$
$522$	1.38602e6	−	2.40066e6i	0.222635	−	0.385616i
$523$	1.00638e7	+	7.31180e6i	1.60882	+	1.16888i	0.867035	+	0.498247i	$0.166023\pi$
$523$	1.00638e7	+	7.31180e6i	1.60882	+	1.16888i	0.741790	+	0.670632i	$0.233977\pi$
$524$	295556.	−	328249.i	0.0470232	−	0.0522245i
$525$	19047.6	−	58622.6i	0.00301608	−	0.00928253i
$526$	−2.40683e6			−0.379298
$527$	2.87665e6	+	1.18087e6i	0.451192	+	0.185215i
$528$	67597.6			0.0105523
$529$	−859417.	+	2.64501e6i	−0.133526	+	0.410950i
$530$	4.29395e6	−	4.76892e6i	0.663999	−	0.737446i
$531$	5.99399e6	+	4.35489e6i	0.922529	+	0.670257i
$532$	−973976.	+	1.68698e6i	−0.149200	+	0.258422i
$533$	−347450.	−	601801.i	−0.0529754	−	0.0917560i
$534$	−5599.29	+	53273.7i	−0.000849728	+	0.00808462i
$535$	−5.27425e6	+	3.83197e6i	−0.796666	+	0.578811i
$536$	397859.	+	3.78537e6i	0.0598159	+	0.569111i
$537$	−154238.	−	171298.i	−0.0230810	−	0.0256341i
$538$	8.41922e6	−	3.74848e6i	1.25405	−	0.558341i
$539$	−3.55522e6	+	755686.i	−0.527102	+	0.112039i
$540$	151249.	+	32149.0i	0.0223208	+	0.00474442i
$541$	5.82369e6	+	2.59287e6i	0.855471	+	0.380880i	0.787134	−	0.616782i	$-0.211564\pi$
$541$	5.82369e6	+	2.59287e6i	0.855471	+	0.380880i	0.0683369	+	0.997662i	$0.478231\pi$
$542$	−903169.	−	2.77967e6i	−0.132060	−	0.406438i
$543$	−15710.8	−	48352.9i	−0.00228664	−	0.00703757i
$544$	543663.	+	242054.i	0.0787649	+	0.0350684i
$545$	−6.35517e6	−	1.35083e6i	−0.916507	−	0.194810i
$546$	−8503.02	+	1807.37i	−0.00122065	+	0.000259458i
$547$	7.19869e6	−	3.20506e6i	1.02869	−	0.458003i	0.178201	−	0.983994i	$-0.442972\pi$
$547$	7.19869e6	−	3.20506e6i	1.02869	−	0.458003i	0.850490	+	0.525991i	$0.176306\pi$
$548$	−625008.	−	694142.i	−0.0889066	−	0.0987408i
$549$	−448226.	−	4.26459e6i	−0.0634697	−	0.603874i
$550$	2.38358e6	−	1.73178e6i	0.335988	−	0.244110i
$551$	356211.	−	3.38912e6i	0.0499837	−	0.475563i
$552$	−28478.8	−	49326.6i	−0.00397808	−	0.00689023i
$553$	−1.09984e6	+	1.90497e6i	−0.152938	+	0.264897i
$554$	−3.38115e6	−	2.45655e6i	−0.468047	−	0.340056i
$555$	−21307.6	+	23664.5i	−0.00293632	+	0.00326111i
$556$	1.08252e6	−	3.33166e6i	0.148508	−	0.457060i
$557$	2.16770e6			0.296047			0.148023	−	0.988984i	$-0.452709\pi$
$557$	2.16770e6			0.296047			0.148023	+	0.988984i	$0.452709\pi$
$558$	5.11214e6	+	930710.i	0.695051	+	0.126540i
$559$	−575599.			−0.0779096
$560$	−344779.	+	1.06112e6i	−0.0464591	+	0.142986i
$561$	−102684.	+	114042.i	−0.0137751	+	0.0152988i
$562$	−2.45759e6	−	1.78555e6i	−0.328223	−	0.238468i
$563$	−6.73468e6	+	1.16648e7i	−0.895460	+	1.55098i	−0.0622251	+	0.998062i	$0.519820\pi$
$563$	−6.73468e6	+	1.16648e7i	−0.895460	+	1.55098i	−0.833235	+	0.552920i	$0.813514\pi$
$564$	17851.8	+	30920.2i	0.00236311	+	0.00409303i
$565$	709849.	−	6.75376e6i	0.0935503	−	0.890071i
$566$	−2.85936e6	+	2.07744e6i	−0.375169	+	0.272576i
$567$	−627756.	−	5.97270e6i	−0.0820037	−	0.780213i
$568$	−873280.	−	969876.i	−0.113575	−	0.126138i
$569$	102041.	−	45431.7i	0.0132128	−	0.00588272i	−0.400120	−	0.916463i	$-0.631031\pi$
$569$	102041.	−	45431.7i	0.0132128	−	0.00588272i	0.413332	+	0.910580i	$0.364365\pi$
$570$	92927.1	−	19752.3i	0.0119800	−	0.00254642i
$571$	5.82498e6	+	1.23814e6i	0.747660	+	0.158920i	0.565958	−	0.824434i	$-0.308506\pi$
$571$	5.82498e6	+	1.23814e6i	0.747660	+	0.158920i	0.181701	+	0.983354i	$0.441840\pi$
$572$	−379589.	−	169004.i	−0.0485091	−	0.0215977i
$573$	−18510.7	−	56970.2i	−0.00235525	−	0.00724872i
$574$	−1.91330e6	−	5.88855e6i	−0.242384	−	0.745982i
$575$	−2.26790e6	−	1.00973e6i	−0.286058	−	0.127361i
$576$	972710.	+	206756.i	0.122159	+	0.0259658i
$577$	−5.02182e6	+	1.06742e6i	−0.627945	+	0.133474i	−0.510882	−	0.859651i	$-0.670681\pi$
$577$	−5.02182e6	+	1.06742e6i	−0.627945	+	0.133474i	−0.117063	+	0.993125i	$0.537348\pi$
$578$	3.95420e6	−	1.76052e6i	0.492311	−	0.219191i
$579$	−111911.	−	124290.i	−0.0138732	−	0.0154078i
$580$	−204027.	−	1.94119e6i	−0.0251836	−	0.239606i
$581$	−374485.	+	272079.i	−0.0460250	+	0.0334391i
$582$	24035.2	−	228680.i	0.00294131	−	0.0279847i
$583$	1.06468e7	+	1.84409e7i	1.29733	+	2.24704i
$584$	459586.	−	796027.i	0.0557616	−	0.0965818i
$585$	−384304.	−	279214.i	−0.0464286	−	0.0337324i
$586$	−7.19222e6	+	7.98777e6i	−0.865205	+	0.960908i
$587$	−3.07424e6	+	9.46153e6i	−0.368250	+	1.13336i	0.579671	+	0.814850i	$0.303181\pi$
$587$	−3.07424e6	+	9.46153e6i	−0.368250	+	1.13336i	−0.947921	+	0.318505i	$0.896819\pi$
$588$	47722.2			0.00569217
$589$	6.20660e6	−	1.51092e6i	0.737167	−	0.179454i
$590$	5.21689e6			0.616995
$591$	−49708.8	+	152988.i	−0.00585416	+	0.0180172i
$592$	−274188.	+	304517.i	−0.0321547	+	0.0357114i
$593$	−6.59714e6	−	4.79311e6i	−0.770405	−	0.559732i	0.131679	−	0.991292i	$-0.457963\pi$
$593$	−6.59714e6	−	4.79311e6i	−0.770405	−	0.559732i	−0.902084	+	0.431560i	$0.857963\pi$
$594$	−256545.	+	444349.i	−0.0298330	+	0.0516723i
$595$	−1.26645e6	−	2.19356e6i	−0.146655	−	0.254013i
$596$	44132.6	−	419893.i	0.00508913	−	0.0484199i
$597$	187454.	−	136194.i	0.0215258	−	0.0156394i
$598$	36596.4	+	348191.i	0.00418490	+	0.0398167i
$599$	4.33334e6	+	4.81266e6i	0.493464	+	0.548047i	0.937511	−	0.347956i	$-0.113124\pi$
$599$	4.33334e6	+	4.81266e6i	0.493464	+	0.548047i	−0.444047	+	0.896004i	$0.646458\pi$
$600$	−35339.6	+	15734.2i	−0.00400759	+	0.00178429i
$601$	1.60586e7	−	3.41335e6i	1.81351	−	0.385474i	0.828784	−	0.559568i	$-0.189033\pi$
$601$	1.60586e7	−	3.41335e6i	1.81351	−	0.385474i	0.984729	+	0.174094i	$0.0556997\pi$
$602$	−5.01654e6	−	1.06630e6i	−0.564174	−	0.119919i
$603$	−1.31906e7	−	5.87282e6i	−1.47730	−	0.657738i
$604$	−1.99183e6	−	6.13022e6i	−0.222157	−	0.683729i
$605$	−2.12263e6	−	6.53279e6i	−0.235769	−	0.725622i
$606$	−176964.	−	78789.6i	−0.0195751	−	0.00871540i
$607$	−1.63832e6	−	348235.i	−0.180479	−	0.0383620i	0.116786	−	0.993157i	$-0.462741\pi$
$607$	−1.63832e6	−	348235.i	−0.180479	−	0.0383620i	−0.297265	+	0.954795i	$0.596074\pi$
$608$	1.19579e6	−	254173.i	0.131189	−	0.0278850i
$609$	123787.	−	55113.3i	0.0135248	−	0.00602162i
$610$	−2.02035e6	−	2.24383e6i	−0.219838	−	0.244154i
$611$	−22940.3	−	218262.i	−0.00248597	−	0.0236524i
$612$	−1.82640e6	+	1.32696e6i	−0.197114	+	0.143212i
$613$	393542.	−	3.74430e6i	0.0422999	−	0.402457i	−0.952801	−	0.303595i	$-0.901813\pi$
$613$	393542.	−	3.74430e6i	0.0422999	−	0.402457i	0.995101	−	0.0988620i	$-0.0315202\pi$
$614$	−1.02672e6	−	1.77833e6i	−0.109908	−	0.190367i
$615$	−150984.	+	261512.i	−0.0160969	+	0.0278807i
$616$	−2.99517e6	−	2.17612e6i	−0.318031	−	0.231063i
$617$	−1.19750e7	+	1.32996e7i	−1.26638	+	1.40646i	−0.392910	+	0.919577i	$0.628532\pi$
$617$	−1.19750e7	+	1.32996e7i	−1.26638	+	1.40646i	−0.873469	+	0.486880i	$0.838135\pi$
$618$	37261.6	−	114680.i	0.00392456	−	0.0120785i
$619$	−1.58362e7			−1.66121			−0.830606	−	0.556860i	$-0.812006\pi$
$619$	−1.58362e7			−1.66121			−0.830606	+	0.556860i	$0.812006\pi$
$620$	3.29734e6	−	1.58561e6i	0.344497	−	0.165660i
$621$	432328.			0.0449867
$622$	−1.98889e6	+	6.12118e6i	−0.206127	+	0.634394i
$623$	1.96310e6	−	2.18024e6i	0.202638	−	0.225053i
$624$	4413.67	+	3206.72i	0.000453772	+	0.000329685i
$625$	2.01090e6	−	3.48298e6i	0.205916	−	0.356657i
$626$	−3.12476e6	−	5.41225e6i	−0.318699	−	0.552004i
$627$	−32951.6	+	313514.i	−0.00334740	+	0.0318484i
$628$	3.39225e6	−	2.46462e6i	0.343233	−	0.249374i
$629$	−97237.2	−	925150.i	−0.00979954	−	0.0932364i
$630$	−2.83210e6	−	3.14536e6i	−0.284287	−	0.315733i
$631$	−9.01357e6	+	4.01310e6i	−0.901204	+	0.401242i	−0.804418	−	0.594063i	$-0.797523\pi$
$631$	−9.01357e6	+	4.01310e6i	−0.901204	+	0.401242i	−0.0967859	+	0.995305i	$0.530856\pi$
$632$	1.35032e6	−	287019.i	0.134476	−	0.0285837i
$633$	−76649.9	−	16292.4i	−0.00760330	−	0.00161613i
$634$	−9.46777e6	−	4.21532e6i	−0.935459	−	0.416493i
$635$	3.11386e6	+	9.58346e6i	0.306453	+	0.943166i
$636$	−86395.6	−	265898.i	−0.00846933	−	0.0260659i
$637$	−267981.	−	119313.i	−0.0261671	−	0.0116503i
$638$	6.33522e6	+	1.34659e6i	0.616184	+	0.130974i
$639$	4.84268e6	−	1.02934e6i	0.469174	−	0.0997260i
$640$	639679.	−	284803.i	0.0617322	−	0.0274850i
$641$	−1.25311e7	−	1.39172e7i	−1.20460	−	1.33785i	−0.926038	−	0.377431i	$-0.876807\pi$
$641$	−1.25311e7	−	1.39172e7i	−1.20460	−	1.33785i	−0.278566	−	0.960417i	$-0.589859\pi$
$642$	29689.3	+	282475.i	0.00284291	+	0.0270485i
$643$	−1.00834e7	+	7.32605e6i	−0.961793	+	0.698783i	−0.953566	−	0.301183i	$-0.902619\pi$
$643$	−1.00834e7	+	7.32605e6i	−0.961793	+	0.698783i	−0.00822649	+	0.999966i	$0.502619\pi$
$644$	−326075.	+	3.10240e6i	−0.0309815	+	0.294770i
$645$	125063.	+	216616.i	0.0118367	+	0.0205018i
$646$	−1.38765e6	+	2.40349e6i	−0.130828	+	0.226600i
$647$	−3.62656e6	−	2.63485e6i	−0.340592	−	0.247455i	0.404320	−	0.914618i	$-0.367508\pi$
$647$	−3.62656e6	−	2.63485e6i	−0.340592	−	0.247455i	−0.744912	+	0.667163i	$0.767508\pi$
$648$	−2.52197e6	+	2.80093e6i	−0.235941	+	0.262039i
$649$	−5.34932e6	+	1.64635e7i	−0.498525	+	1.53430i
$650$	237785.			0.0220750
$651$	175423.	+	183686.i	0.0162231	+	0.0169873i
$652$	6.11510e6			0.563359
$653$	2.19310e6	−	6.74967e6i	0.201269	−	0.619441i	−0.798577	−	0.601892i	$-0.794414\pi$
$653$	2.19310e6	−	6.74967e6i	0.201269	−	0.619441i	0.999846	−	0.0175488i	$-0.00558624\pi$
$654$	−189407.	+	210358.i	−0.0173162	+	0.0192316i
$655$	954506.	+	693489.i	0.0869312	+	0.0631592i
$656$	−1.94287e6	+	3.36516e6i	−0.176273	+	0.305313i
$657$	1.74344e6	+	3.01972e6i	0.157577	+	0.272931i
$658$	204399.	−	1.94473e6i	0.0184041	−	0.175103i
$659$	−4.04601e6	+	2.93960e6i	−0.362922	+	0.263678i	−0.754270	−	0.656565i	$-0.772009\pi$
$659$	−4.04601e6	+	2.93960e6i	−0.362922	+	0.263678i	0.391348	+	0.920243i	$0.372009\pi$
$660$	18873.7	+	179571.i	0.00168654	+	0.0160464i
$661$	4.70103e6	+	5.22102e6i	0.418494	+	0.464785i	0.915121	−	0.403179i	$-0.132095\pi$
$661$	4.70103e6	+	5.22102e6i	0.418494	+	0.464785i	−0.496627	+	0.867964i	$0.665428\pi$
$662$	9.23688e6	−	4.11252e6i	0.819182	−	0.364723i
$663$	−12114.5	+	2575.02i	−0.00107034	+	0.000227508i
$664$	284154.	+	60398.8i	0.0250111	+	0.00531628i
$665$	−4.75335e6	−	2.11633e6i	−0.416818	−	0.185579i
$666$	−480352.	−	1.47837e6i	−0.0419637	−	0.129151i
$667$	−1.68640e6	−	5.19020e6i	−0.146773	−	0.451720i
$668$	5.43356e6	+	2.41917e6i	0.471132	+	0.209762i
$669$	−333606.	−	70910.2i	−0.0288183	−	0.00612552i
$670$	−9.94467e6	+	2.11380e6i	−0.855861	+	0.181919i
$671$	9.15272e6	−	4.07506e6i	0.784773	−	0.349403i
$672$	32526.2	+	36123.9i	0.00277849	+	0.00308583i
$673$	1.92881e6	+	1.83514e7i	0.164154	+	1.56182i	0.697913	+	0.716183i	$0.254112\pi$
$673$	1.92881e6	+	1.83514e7i	0.164154	+	1.56182i	−0.533759	+	0.845637i	$0.679221\pi$
$674$	−3.94201e6	+	2.86404e6i	−0.334247	+	0.242845i
$675$	30692.2	−	292017.i	0.00259280	−	0.0246689i
$676$	2.95358e6	+	5.11574e6i	0.248589	+	0.430568i
$677$	1.07131e7	−	1.85557e7i	0.898347	−	1.55598i	0.0687398	−	0.997635i	$-0.478102\pi$
$677$	1.07131e7	−	1.85557e7i	0.898347	−	1.55598i	0.829607	−	0.558348i	$-0.188564\pi$
$678$	−239360.	−	173906.i	−0.0199976	−	0.0145291i
$679$	−8.42669e6	+	9.35879e6i	−0.701427	+	0.779014i
$680$	−491218.	+	1.51181e6i	−0.0407382	+	0.125379i
$681$	−383921.			−0.0317230
$682$	1.62285e6	+	1.20317e7i	0.133604	+	0.990523i
$683$	−3.17711e6			−0.260604			−0.130302	−	0.991474i	$-0.541595\pi$
$683$	−3.17711e6			−0.260604			−0.130302	+	0.991474i	$0.541595\pi$
$684$	−1.43309e6	+	4.41059e6i	−0.117120	+	0.360459i
$685$	1.66947e6	−	1.85413e6i	0.135941	−	0.150978i
$686$	−7.66096e6	−	5.56601e6i	−0.621546	−	0.451579i
$687$	−266392.	+	461404.i	−0.0215342	+	0.0372984i
$688$	1.60932e6	+	2.78743e6i	0.129620	+	0.224508i
$689$	−179637.	+	1.70913e6i	−0.0144161	+	0.137160i
$690$	123084.	−	89425.5i	0.00984187	−	0.00715054i
$691$	−1.74042e6	−	1.65590e7i	−0.138662	−	1.31928i	−0.813607	−	0.581416i	$-0.802499\pi$
$691$	−1.74042e6	−	1.65590e7i	−0.138662	−	1.31928i	0.674944	−	0.737869i	$-0.264168\pi$
$692$	2.87762e6	+	3.19593e6i	0.228438	+	0.253706i
$693$	1.28302e7	−	5.71236e6i	1.01484	−	0.451838i
$694$	1.28485e7	−	2.73103e6i	1.01264	−	0.215243i
$695$	9.15272e6	+	1.94547e6i	0.718767	+	0.152779i
$696$	−77686.6	−	34588.3i	−0.00607888	−	0.00270649i
$697$	−2.72594e6	−	8.38959e6i	−0.212537	−	0.654122i
$698$	−1.22250e6	−	3.76247e6i	−0.0949751	−	0.292303i
$699$	268319.	+	119463.i	0.0207711	+	0.00924787i
$700$	2.07237e6	+	440497.i	0.159854	+	0.0339780i
$701$	1.43002e7	−	3.03960e6i	1.09913	−	0.233626i	0.377569	−	0.925981i	$-0.376760\pi$
$701$	1.43002e7	−	3.03960e6i	1.09913	−	0.233626i	0.721557	+	0.692355i	$0.243427\pi$
$702$	−37829.9	+	16842.9i	−0.00289729	+	0.00128996i
$703$	−1.27868e6	−	1.42011e6i	−0.0975825	−	0.108376i
$704$	242868.	+	2.31074e6i	0.0184688	+	0.175719i
$705$	−77154.6	+	56056.1i	−0.00584640	+	0.00424766i
$706$	302543.	−	2.87850e6i	0.0228441	−	0.217348i
$707$	5.30466e6	+	9.18795e6i	0.399125	+	0.691305i
$708$	113644.	−	196836.i	0.00852043	−	0.0147578i
$709$	2.06823e7	+	1.50266e7i	1.54519	+	1.12265i	0.946971	+	0.321320i	$0.104126\pi$
$709$	2.06823e7	+	1.50266e7i	1.54519	+	1.12265i	0.598223	+	0.801329i	$0.295874\pi$
$710$	2.33263e6	−	2.59065e6i	0.173660	−	0.192869i
$711$	−1.61828e6	+	4.98054e6i	−0.120055	+	0.369490i
$712$	−1.84121e6			−0.136114
$713$	8.09592e6	−	6.25313e6i	0.596407	−	0.460653i
$714$	−110352.			−0.00810095
$715$	342971.	−	1.05556e6i	0.0250895	−	0.0772176i
$716$	5.30146e6	−	5.88787e6i	0.386468	−	0.429216i
$717$	332504.	+	241578.i	0.0241545	+	0.0175493i
$718$	−7.69797e6	+	1.33333e7i	−0.557269	+	0.965218i
$719$	−4.41355e6	−	7.64449e6i	−0.318395	−	0.551476i	0.661759	−	0.749717i	$-0.269810\pi$
$719$	−4.41355e6	−	7.64449e6i	−0.318395	−	0.551476i	−0.980153	+	0.198241i	$0.936477\pi$
$720$	−277655.	+	2.64171e6i	−0.0199606	+	0.189913i
$721$	−5.34281e6	+	3.88178e6i	−0.382764	+	0.278094i
$722$	−439359.	−	4.18022e6i	−0.0313672	−	0.298439i
$723$	−320580.	−	356041.i	−0.0228082	−	0.0253311i
$724$	1.59644e6	−	710779.i	0.113189	−	0.0503951i
$725$	−3.62546e6	+	770614.i	−0.256164	+	0.0544493i
$726$	−292725.	−	62220.7i	−0.0206119	−	0.00438120i
$727$	7.50401e6	+	3.34100e6i	0.526571	+	0.234445i	0.652764	−	0.757561i	$-0.273609\pi$
$727$	7.50401e6	+	3.34100e6i	0.526571	+	0.234445i	−0.126193	+	0.992006i	$0.540276\pi$
$728$	−92332.9	−	284172.i	−0.00645696	−	0.0198725i
$729$	−4.41035e6	−	1.35737e7i	−0.307365	−	0.945972i
$730$	2.24295e6	+	998624.i	0.155780	+	0.0693577i
$731$	−7.14722e6	−	1.51919e6i	−0.494702	−	0.105152i
$732$	−128672.	+	27350.0i	−0.00887576	+	0.00188660i
$733$	−2.86038e6	+	1.27352e6i	−0.196636	+	0.0875480i	−0.502692	−	0.864465i	$-0.667657\pi$
$733$	−2.86038e6	+	1.27352e6i	−0.196636	+	0.0875480i	0.306056	+	0.952013i	$0.400990\pi$
$734$	6.25408e6	+	6.94586e6i	0.428473	+	0.475867i
$735$	13324.4	+	126773.i	0.000909764	+	0.00865583i
$736$	1.58385e6	−	1.15073e6i	0.107775	−	0.0783033i
$737$	3.52635e6	−	3.35510e7i	0.239142	−	2.27529i
$738$	−7.37027e6	−	1.27657e7i	−0.498130	−	0.862787i
$739$	2.77184e6	−	4.80098e6i	0.186706	−	0.323384i	−0.757444	−	0.652900i	$-0.773552\pi$
$739$	2.77184e6	−	4.80098e6i	0.186706	−	0.323384i	0.944150	+	0.329516i	$0.106886\pi$
$740$	−885498.	−	643352.i	−0.0594440	−	0.0431886i
$741$	−17024.1	+	18907.2i	−0.00113899	+	0.00126497i
$742$	−4.73177e6	+	1.45629e7i	−0.315511	+	0.971042i
$743$	−1.67307e7			−1.11184			−0.555919	−	0.831236i	$-0.687634\pi$
$743$	−1.67307e7			−1.11184			−0.555919	+	0.831236i	$0.687634\pi$
$744$	12002.4	−	158951.i	0.000794942	−	0.0105277i
$745$	1.12776e6			0.0744433
$746$	−5.09043e6	+	1.56667e7i	−0.334894	+	1.03070i
$747$	−737393.	+	818958.i	−0.0483501	+	0.0536983i
$748$	−4.26730e6	−	3.10038e6i	−0.278869	−	0.202610i
$749$	7.77800e6	−	1.34719e7i	0.506598	−	0.877454i
$750$	−176003.	−	304847.i	−0.0114253	−	0.0197892i
$751$	616722.	−	5.86772e6i	0.0399015	−	0.379638i	−0.956288	−	0.292426i	$-0.905538\pi$
$751$	616722.	−	5.86772e6i	0.0399015	−	0.379638i	0.996190	−	0.0872120i	$-0.0277958\pi$
$752$	−992831.	+	721334.i	−0.0640222	+	0.0465148i
$753$	67864.1	+	645684.i	0.00436167	+	0.0414985i
$754$	349768.	+	388456.i	0.0224053	+	0.0248836i
$755$	1.57287e7	−	7.00285e6i	1.00421	−	0.447103i
$756$	−360902.	+	76712.0i	−0.0229659	+	0.00488156i
$757$	2.24299e7	+	4.76762e6i	1.42262	+	0.302386i	0.854024	−	0.520233i	$-0.174155\pi$
$757$	2.24299e7	+	4.76762e6i	1.42262	+	0.302386i	0.568592	+	0.822620i	$0.307488\pi$
$758$	1.32674e7	+	5.90702e6i	0.838710	+	0.373418i
$759$	156002.	+	480124.i	0.00982936	+	0.0302517i
$760$	1.00908e6	+	3.10563e6i	0.0633711	+	0.195036i
$761$	−2.42015e7	−	1.07752e7i	−1.51489	−	0.674471i	−0.530053	−	0.847965i	$-0.677828\pi$
$761$	−2.42015e7	−	1.07752e7i	−1.51489	−	0.674471i	−0.984835	+	0.173493i	$0.944495\pi$
$762$	429421.	+	91276.3i	0.0267915	+	0.00569470i
$763$	1.51643e7	−	3.22327e6i	0.942998	−	0.200440i
$764$	1.88095e6	−	837452.i	0.116585	−	0.0519071i
$765$	−4.03498e6	−	4.48130e6i	−0.249280	−	0.276854i
$766$	1.77945e6	+	1.69304e7i	0.109576	+	1.04254i
$767$	−1.13028e6	+	821194.i	−0.0693739	+	0.0504031i
$768$	3188.81	−	30339.5i	0.000195086	−	0.00185612i
$769$	−1.65220e6	−	2.86169e6i	−0.100750	−	0.174505i	0.811244	−	0.584708i	$-0.198791\pi$
$769$	−1.65220e6	−	2.86169e6i	−0.100750	−	0.174505i	−0.911994	+	0.410203i	$0.865458\pi$
$770$	4.94453e6	−	8.56418e6i	0.300537	−	0.520546i
$771$	−195319.	−	141908.i	−0.0118334	−	0.00859745i
$772$	3.84662e6	−	4.27211e6i	0.232293	−	0.257988i
$773$	−7.63941e6	+	2.35117e7i	−0.459845	+	1.41526i	0.405507	+	0.914092i	$0.367095\pi$
$773$	−7.63941e6	+	2.35117e7i	−0.459845	+	1.41526i	−0.865352	+	0.501165i	$0.832905\pi$
$774$	−1.22099e7			−0.732588
$775$	−3.64894e6	−	5.91234e6i	−0.218229	−	0.353594i
$776$	7.90349e6			0.471156
$777$	23480.2	−	72264.7i	0.00139524	−	0.00429411i
$778$	1.08209e7	−	1.20179e7i	0.640939	−	0.711834i
$779$	−1.46603e7	−	1.06514e7i	−0.865566	−	0.628870i
$780$	−7286.24	+	12620.1i	−0.000428812	+	0.000742725i
$781$	5.78374e6	+	1.00177e7i	0.339298	+	0.587682i
$782$	−464569.	+	4.42008e6i	−0.0271665	+	0.258472i
$783$	522199.	−	379400.i	0.0304391	−	0.0221153i
$784$	171459.	+	1.63132e6i	0.00996255	+	0.0947873i
$785$	7.49434e6	+	8.32331e6i	0.434069	+	0.482083i
$786$	46958.5	−	20907.3i	0.00271118	−	0.00120709i
$787$	1.33172e7	−	2.83065e6i	0.766434	−	0.162910i	0.191926	−	0.981409i	$-0.438527\pi$
$787$	1.33172e7	−	2.83065e6i	0.766434	−	0.162910i	0.574508	+	0.818499i	$0.305193\pi$
$788$	−5.40829e6	−	1.14957e6i	−0.310274	−	0.0659507i
$789$	−255876.	−	113923.i	−0.0146331	−	0.00651509i
$790$	1.13948e6	+	3.50695e6i	0.0649588	+	0.199923i
$791$	5.00736e6	+	1.54111e7i	0.284556	+	0.875774i
$792$	−8.05203e6	−	3.58499e6i	−0.456134	−	0.203084i
$793$	790925.	+	168116.i	0.0446635	+	0.00949352i
$794$	−2.04839e6	+	435398.i	−0.115308	+	0.0245095i
$795$	682231.	−	303749.i	0.0382837	−	0.0170450i
$796$	5.32910e6	+	5.91857e6i	0.298107	+	0.331081i
$797$	−1.87951e6	−	1.78823e7i	−0.104809	−	0.997191i	−0.912914	−	0.408152i	$-0.866173\pi$
$797$	−1.87951e6	−	1.78823e7i	−0.104809	−	0.997191i	0.808105	−	0.589039i	$-0.200493\pi$
$798$	−183396.	+	133245.i	−0.0101949	+	0.00740704i
$799$	291214.	−	2.77071e6i	0.0161378	−	0.153541i
$800$	−664824.	−	1.15151e6i	−0.0367267	−	0.0636125i
$801$	3.49231e6	−	6.04885e6i	0.192323	−	0.333113i
$802$	−1.51677e7	−	1.10200e7i	−0.832693	−	0.604987i
$803$	−5.45135e6	+	6.05434e6i	−0.298343	+	0.331343i
$804$	−136877.	+	421265.i	−0.00746778	+	0.0229835i
$805$	−8.33249e6			−0.453195
$806$	−464801.	+	862572.i	−0.0252017	+	0.0467690i
$807$	1.07250e6			0.0579712
$808$	2.05752e6	−	6.33238e6i	0.110870	−	0.341223i
$809$	−8.42190e6	+	9.35347e6i	−0.452417	+	0.502460i	−0.925599	−	0.378505i	$-0.876438\pi$
$809$	−8.42190e6	+	9.35347e6i	−0.452417	+	0.502460i	0.473183	+	0.880964i	$0.343105\pi$
$810$	−8.14477e6	−	5.91752e6i	−0.436181	−	0.316904i
$811$	−4.39191e6	+	7.60701e6i	−0.234478	+	0.406127i	−0.959121	−	0.282997i	$-0.908671\pi$
$811$	−4.39191e6	+	7.60701e6i	−0.234478	+	0.406127i	0.724643	+	0.689124i	$0.242005\pi$
$812$	2.32873e6	+	4.03347e6i	0.123945	+	0.214679i
$813$	35553.0	−	338264.i	0.00188647	−	0.0179485i
$814$	2.93827e6	−	2.13478e6i	0.155429	−	0.112925i
$815$	1.70738e6	+	1.62446e7i	0.0900401	+	0.856675i
$816$	46341.0	+	51466.9i	0.00243635	+	0.00270584i
$817$	−1.37124e7	+	6.10517e6i	−0.718720	+	0.319995i
$818$	1.86643e7	−	3.96722e6i	0.975277	−	0.207302i
$819$	1.10871e6	+	235663.i	0.0577574	+	0.0122767i
$820$	−9.48193e6	−	4.22163e6i	−0.492450	−	0.219253i
$821$	−1.86788e6	−	5.74874e6i	−0.0967143	−	0.297656i	0.890982	−	0.454038i	$-0.150017\pi$
$821$	−1.86788e6	−	5.74874e6i	−0.0967143	−	0.297656i	−0.987697	+	0.156382i	$0.950017\pi$
$822$	−33590.1	−	103380.i	−0.00173393	−	0.00533650i
$823$	−2.28742e7	−	1.01843e7i	−1.17719	−	0.524119i	−0.277533	−	0.960716i	$-0.589517\pi$
$823$	−2.28742e7	−	1.01843e7i	−1.17719	−	0.524119i	−0.899657	+	0.436597i	$0.856183\pi$
$824$	4.05405e6	+	861715.i	0.208004	+	0.0442126i
$825$	335376.	−	71286.4i	0.0171553	−	0.00364646i
$826$	−1.13720e7	+	5.06314e6i	−0.579945	+	0.258208i
$827$	1.42819e6	+	1.58616e6i	0.0726141	+	0.0806461i	0.778357	−	0.627822i	$-0.216053\pi$
$827$	1.42819e6	+	1.58616e6i	0.0726141	+	0.0806461i	−0.705743	+	0.708468i	$0.749387\pi$
$828$	776300.	+	7.38600e6i	0.0393508	+	0.374398i
$829$	1.34435e7	−	9.76729e6i	0.679402	−	0.493614i	−0.193757	−	0.981049i	$-0.562067\pi$
$829$	1.34435e7	−	9.76729e6i	0.679402	−	0.493614i	0.873159	+	0.487435i	$0.162067\pi$
$830$	−81110.2	+	771712.i	−0.00408677	+	0.0388830i
$831$	−243182.	−	421204.i	−0.0122160	−	0.0211587i
$832$	−93759.9	+	162397.i	−0.00469579	+	0.00813335i
$833$	−3.01261e6	−	2.18879e6i	−0.150429	−	0.109293i
$834$	272785.	−	302958.i	0.0135802	−	0.0150823i
$835$	−4.90940e6	+	1.51096e7i	−0.243675	+	0.749956i
$836$	−1.08355e7			−0.536206
$837$	999308.	+	682147.i	0.0493044	+	0.0336561i
$838$	−451941.			−0.0222317
$839$	−2.53923e6	+	7.81496e6i	−0.124537	+	0.383285i	−0.993816	−	0.111036i	$-0.964583\pi$
$839$	−2.53923e6	+	7.81496e6i	−0.124537	+	0.383285i	0.869280	+	0.494321i	$0.164583\pi$
$840$	−86880.9	+	96491.0i	−0.00424841	+	0.00471833i
$841$	1.00021e7	+	7.26697e6i	0.487643	+	0.354294i
$842$	3.57449e6	−	6.19120e6i	0.173754	−	0.300950i
$843$	−176757.	−	306153.i	−0.00856660	−	0.0148378i
$844$	281544.	−	2.67871e6i	0.0136048	−	0.129441i
$845$	−1.27652e7	+	9.27446e6i	−0.615015	+	0.446835i
$846$	−486621.	−	4.62989e6i	−0.0233757	−	0.222405i
$847$	1.09673e7	+	1.21804e7i	0.525279	+	0.583382i
$848$	8.77899e6	−	3.90866e6i	0.419233	−	0.186654i
$849$	−402318.	+	85515.4i	−0.0191558	+	0.00407169i
$850$	2.95257e6	+	627589.i	0.140170	+	0.0297940i
$851$	−2.79566e6	−	1.24471e6i	−0.132331	−	0.0589174i
$852$	−46933.2	−	144445.i	−0.00221504	−	0.00681718i
$853$	1.04954e7	+	3.23015e7i	0.493886	+	1.52003i	0.818685	+	0.574242i	$0.194703\pi$
$853$	1.04954e7	+	3.23015e7i	0.493886	+	1.52003i	−0.324799	+	0.945783i	$0.605297\pi$
$854$	6.58175e6	+	2.93038e6i	0.308814	+	0.137493i
$855$	−1.21168e7	−	2.57550e6i	−0.566854	−	0.120488i
$856$	−9.54939e6	+	2.02979e6i	−0.445442	+	0.0946816i
$857$	−2.43783e7	+	1.08539e7i	−1.13384	+	0.504818i	−0.885862	−	0.463948i	$-0.846432\pi$
$857$	−2.43783e7	+	1.08539e7i	−1.13384	+	0.504818i	−0.247977	+	0.968766i	$0.579766\pi$
$858$	−32355.6	−	35934.5i	−0.00150048	−	0.00166645i
$859$	−901721.	−	8.57931e6i	−0.0416955	−	0.396706i	−0.995389	−	0.0959249i	$-0.969419\pi$
$859$	−901721.	−	8.57931e6i	−0.0416955	−	0.396706i	0.953693	−	0.300782i	$-0.0972475\pi$
$860$	−6.95541e6	+	5.05340e6i	−0.320683	+	0.232990i
$861$	75316.7	−	716590.i	0.00346245	−	0.0329430i
$862$	9.66484e6	+	1.67400e7i	0.443023	+	0.767338i
$863$	1.02508e7	−	1.77550e7i	0.468525	−	0.811509i	−0.530828	−	0.847480i	$-0.678119\pi$
$863$	1.02508e7	−	1.77550e7i	0.468525	−	0.811509i	0.999353	+	0.0359707i	$0.0114523\pi$
$864$	187333.	+	136106.i	0.00853750	+	0.00620286i
$865$	−7.68645e6	+	8.53667e6i	−0.349290	+	0.387925i
$866$	2.99660e6	−	9.22257e6i	0.135779	−	0.417885i
$867$	503714.			0.0227581
$868$	−5.64881e6	+	6.65656e6i	−0.254482	+	0.299882i
$869$	−1.22357e7			−0.549640
$870$	70192.4	−	216030.i	0.00314407	−	0.00967645i
$871$	1.82185e6	−	2.02337e6i	0.0813705	−	0.0903711i
$872$	−7.87134e6	−	5.71886e6i	−0.350556	−	0.254694i
$873$	−1.49909e7	+	2.59650e7i	−0.665721	+	1.15306i
$874$	4.56497e6	+	7.90675e6i	0.202143	+	0.350122i
$875$	−2.01520e6	+	1.91733e7i	−0.0889811	+	0.846598i
$876$	86538.5	−	62873.9i	0.00381021	−	0.00276828i
$877$	466924.	+	4.44249e6i	0.0204997	+	0.195042i	0.999979	−	0.00650390i	$-0.00207027\pi$
$877$	466924.	+	4.44249e6i	0.0204997	+	0.195042i	−0.979479	+	0.201546i	$0.935404\pi$
$878$	−1.65774e7	−	1.84111e7i	−0.725738	−	0.806013i
$879$	−1.14271e6	+	508769.i	−0.0498844	+	0.0222100i
$880$	−6.07061e6	+	1.29035e6i	−0.264256	+	0.0561694i
$881$	−2.58544e7	−	5.49553e6i	−1.12226	−	0.238545i	−0.390834	−	0.920461i	$-0.627813\pi$
$881$	−2.58544e7	−	5.49553e6i	−1.12226	−	0.238545i	−0.731430	+	0.681916i	$0.761147\pi$
$882$	−5.68454e6	−	2.53092e6i	−0.246050	−	0.109549i
$883$	−2.19682e6	−	6.76113e6i	−0.0948186	−	0.291822i	0.892388	−	0.451269i	$-0.149029\pi$
$883$	−2.19682e6	−	6.76113e6i	−0.0948186	−	0.291822i	−0.987206	+	0.159448i	$0.949029\pi$
$884$	−131550.	−	404868.i	−0.00566185	−	0.0174254i
$885$	554621.	+	246933.i	0.0238034	+	0.0105979i
$886$	−3.80855e6	−	809533.i	−0.162996	−	0.0346458i
$887$	8.43029e6	−	1.79191e6i	0.359777	−	0.0764730i	−0.0244770	−	0.999700i	$-0.507792\pi$
$887$	8.43029e6	−	1.79191e6i	0.359777	−	0.0764730i	0.384254	+	0.923227i	$0.374459\pi$
$888$	−43563.5	+	19395.7i	−0.00185392	+	0.000825417i
$889$	−1.60888e7	−	1.78684e7i	−0.682760	−	0.758282i
$890$	−514079.	−	4.89114e6i	−0.0217548	−	0.206983i
$891$	2.70261e7	−	1.96356e7i	1.14048	−	0.828610i
$892$	1.22538e6	−	1.16587e7i	0.0515653	−	0.490611i
$893$	−2.86153e6	−	4.95632e6i	−0.120080	−	0.207984i
$894$	24566.9	−	42551.0i	0.00102803	−	0.00178060i
$895$	1.71212e7	+	1.24393e7i	0.714458	+	0.519084i
$896$	−1.11799e6	+	1.24165e6i	−0.0465230	+	0.0516690i
$897$	−12590.4	+	38749.4i	−0.000522468	+	0.00160799i
$898$	1.11222e7			0.460255
$899$	4.29129e6	−	1.46578e7i	0.177088	−	0.604880i
$900$	5.04401e6			0.207572
$901$	−6.74150e6	+	2.07482e7i	−0.276659	+	0.851469i
$902$	2.30453e7	−	2.55944e7i	0.943117	−	1.04744i
$903$	−482850.	−	350811.i	−0.0197058	−	0.0143171i
$904$	5.08475e6	−	8.80705e6i	0.206942	−	0.358434i
$905$	2.33390e6	+	4.04244e6i	0.0947243	+	0.164067i
$906$	78407.8	−	746001.i	0.00317350	−	0.0301939i
$907$	−767484.	+	557610.i	−0.0309778	+	0.0225067i	−0.603166	−	0.797615i	$-0.706095\pi$
$907$	−767484.	+	557610.i	−0.0309778	+	0.0225067i	0.572189	+	0.820122i	$0.306095\pi$
$908$	−1.37937e6	−	1.31238e7i	−0.0555222	−	0.528258i
$909$	1.69009e7	+	1.87704e7i	0.678423	+	0.753466i
$910$	729115.	−	324623.i	0.0291872	−	0.0129950i
$911$	5.64092e6	−	1.19901e6i	0.225192	−	0.0478661i	−0.0939334	−	0.995578i	$-0.529944\pi$
$911$	5.64092e6	−	1.19901e6i	0.225192	−	0.0478661i	0.319126	+	0.947712i	$0.396611\pi$
$912$	139159.	+	29579.1i	0.00554017	+	0.00117760i
$913$	−2.35221e6	−	1.04727e6i	−0.0933897	−	0.0415798i
$914$	2.01794e6	+	6.21059e6i	0.0798993	+	0.245905i
$915$	−108581.	−	334177.i	−0.00428746	−	0.0131954i
$916$	−1.67296e7	−	7.44851e6i	−0.658791	−	0.293313i
$917$	−2.75373e6	−	585323.i	−0.108143	−	0.0229865i
$918$	−514188.	+	109294.i	−0.0201379	+	0.00428045i
$919$	3.56043e7	−	1.58520e7i	1.39063	−	0.619151i	0.431503	−	0.902111i	$-0.357983\pi$
$919$	3.56043e7	−	1.58520e7i	1.39063	−	0.619151i	0.959131	+	0.282961i	$0.0913166\pi$
$920$	3.49912e6	+	3.88617e6i	0.136298	+	0.151374i
$921$	−24978.7	−	237657.i	−0.000970335	−	0.00923212i
$922$	−1.92865e7	+	1.40125e7i	−0.747181	+	0.542859i
$923$	−97585.4	+	928463.i	−0.00377034	+	0.0358724i
$924$	−215421.	−	373120.i	−0.00830057	−	0.0143770i
$925$	−1.03921e6	+	1.79997e6i	−0.0399347	+	0.0691689i
$926$	−4.34716e6	−	3.15840e6i	−0.166601	−	0.121043i
$927$	−1.05205e7	+	1.16841e7i	−0.402101	+	0.446578i
$928$	903241.	−	2.77989e6i	0.0344297	−	0.105964i
$929$	1.89675e7			0.721058			0.360529	−	0.932748i	$-0.382596\pi$
$929$	1.89675e7			0.721058			0.360529	+	0.932748i	$0.382596\pi$
$930$	425602.	−	12496.3i	0.0161360	−	0.000473776i
$931$	−7.64958e6			−0.289243
$932$	−3.11967e6	+	9.60136e6i	−0.117644	+	0.362070i
$933$	−501181.	+	556618.i	−0.0188491	+	0.0209340i
$934$	−1.64870e7	−	1.19785e7i	−0.618406	−	0.449298i
$935$	7.04462e6	−	1.22016e7i	0.263529	−	0.456446i
$936$	−355677.	−	616051.i	−0.0132699	−	0.0229841i
$937$	1.53185e6	−	1.45746e7i	0.0569990	−	0.542309i	−0.928344	−	0.371723i	$-0.878767\pi$
$937$	1.53185e6	−	1.45746e7i	0.0569990	−	0.542309i	0.985343	−	0.170586i	$-0.0545662\pi$
$938$	1.96263e7	−	1.42594e7i	0.728336	−	0.529167i
$939$	−76021.5	−	723296.i	−0.00281367	−	0.0267702i
$940$	−2.19341e6	−	2.43603e6i	−0.0809656	−	0.0899214i
$941$	−5.87249e6	+	2.61460e6i	−0.216196	+	0.0962568i	−0.511977	−	0.858999i	$-0.671087\pi$
$941$	−5.87249e6	+	2.61460e6i	−0.216196	+	0.0962568i	0.295781	+	0.955256i	$0.404420\pi$
$942$	477298.	−	101453.i	0.0175252	−	0.00372509i
$943$	−2.83854e7	−	6.03351e6i	−1.03948	−	0.220948i
$944$	7.13691e6	+	3.17756e6i	0.260663	+	0.116055i
$945$	−304550.	−	937308.i	−0.0110938	−	0.0341431i
$946$	−8.81560e6	−	2.71316e7i	−0.320276	−	0.985707i
$947$	2.83608e7	+	1.26270e7i	1.02765	+	0.457537i	0.850126	−	0.526580i	$-0.176526\pi$
$947$	2.83608e7	+	1.26270e7i	1.02765	+	0.457537i	0.177520	+	0.984117i	$0.443193\pi$
$948$	157141.	+	33401.4i	0.00567897	+	0.00120710i
$949$	−643145.	+	136705.i	−0.0231816	+	0.00492740i
$950$	5.66472e6	−	2.52209e6i	0.203643	−	0.0906676i
$951$	−807018.	−	896285.i	−0.0289356	−	0.0321362i
$952$	−396480.	−	3.77226e6i	−0.0141785	−	0.134899i
$953$	−7.39531e6	+	5.37301e6i	−0.263769	+	0.191640i	−0.711807	−	0.702375i	$-0.752123\pi$
$953$	−7.39531e6	+	5.37301e6i	−0.263769	+	0.191640i	0.448038	+	0.894015i	$0.352123\pi$
$954$	−3.81055e6	+	3.62550e7i	−0.135555	+	1.28972i
$955$	2.74985e6	+	4.76287e6i	0.0975664	+	0.168990i
$956$	−7.06341e6	+	1.22342e7i	−0.249959	+	0.432942i
$957$	609776.	+	443028.i	0.0215224	+	0.0156369i
$958$	2.27057e7	−	2.52173e7i	0.799322	−	0.887737i
$959$	−1.83969e6	+	5.66198e6i	−0.0645948	+	0.198802i
$960$	81486.6			0.00285370
$961$	2.85798e7	−	1.67974e6i	0.998277	−	0.0586722i
$962$	293120.			0.0102119
$963$	1.14444e7	−	3.52222e7i	0.397673	−	1.22391i
$964$	1.10190e7	−	1.22378e7i	0.381900	−	0.424143i
$965$	1.24228e7	+	9.02566e6i	0.429437	+	0.312004i
$966$	−181513.	+	314390.i	−0.00625843	+	0.0108399i
$967$	−1.83803e7	−	3.18356e7i	−0.632100	−	1.09483i	−0.987122	−	0.159972i	$-0.948860\pi$
$967$	−1.83803e7	−	3.18356e7i	−0.632100	−	1.09483i	0.355021	−	0.934858i	$-0.384474\pi$
$968$	1.07522e6	−	1.02300e7i	0.0368814	−	0.350903i
$969$	−261290.	+	189839.i	−0.00893952	+	0.00649494i
$970$	2.20671e6	+	2.09954e7i	0.0753036	+	0.716466i
$971$	−7.06027e6	−	7.84122e6i	−0.240311	−	0.266892i	0.610910	−	0.791700i	$-0.290804\pi$
$971$	−7.06027e6	−	7.84122e6i	−0.240311	−	0.266892i	−0.851221	+	0.524808i	$0.824137\pi$
$972$	−1.20388e6	+	536001.i	−0.0408711	+	0.0181970i
$973$	−2.18396e7	+	4.64216e6i	−0.739543	+	0.157195i
$974$	2.89433e7	+	6.15209e6i	0.977577	+	0.207790i
$975$	25279.5	+	11255.2i	0.000851643	+	0.000379176i
$976$	−1.39722e6	−	4.30022e6i	−0.0469507	−	0.144499i
$977$	1.04113e7	+	3.20426e7i	0.348953	+	1.07397i	0.959433	+	0.281936i	$0.0909765\pi$
$977$	1.04113e7	+	3.20426e7i	0.348953	+	1.07397i	−0.610480	+	0.792032i	$0.709023\pi$
$978$	650113.	+	289449.i	0.0217341	+	0.00967665i
$979$	1.59626e7	+	3.39296e6i	0.532289	+	0.113142i
$980$	−4.28570e6	+	910954.i	−0.142547	+	0.0302992i
$981$	3.37178e7	−	1.50122e7i	1.11863	−	0.498047i
$982$	1.09563e7	+	1.21682e7i	0.362564	+	0.402668i
$983$	−2.51968e6	−	2.39732e7i	−0.0831691	−	0.791301i	−0.954018	−	0.299750i	$-0.903097\pi$
$983$	−2.51968e6	−	2.39732e7i	−0.0831691	−	0.791301i	0.870849	−	0.491551i	$-0.163570\pi$
$984$	−365837.	+	265796.i	−0.0120448	+	0.00875106i
$985$	1.54377e6	−	1.46880e7i	0.0506981	−	0.482360i
$986$	3.31781e6	+	5.74661e6i	0.108682	+	0.188243i
$987$	113781.	−	197074.i	0.00371772	−	0.00643928i
$988$	−707483.	−	514017.i	−0.0230581	−	0.0167527i
$989$	−1.60842e7	+	1.78633e7i	−0.522889	+	0.580727i
$990$	7.27527e6	−	2.23910e7i	0.235918	−	0.726081i
$991$	1.02542e7			0.331678			0.165839	−	0.986153i	$-0.446967\pi$
$991$	1.02542e7			0.331678			0.165839	+	0.986153i	$0.446967\pi$
$992$	5.47668e6	−	160803.i	0.176701	−	0.00518817i
$993$	1.17666e6			0.0378684
$994$	−2.57047e6	+	7.91109e6i	−0.0825175	+	0.253963i
$995$	−1.42346e7	+	1.58091e7i	−0.455815	+	0.506233i
$996$	27350.3	+	19871.1i	0.000873602	+	0.000634709i
$997$	−4.30387e6	+	7.45452e6i	−0.137126	+	0.237510i	−0.926408	−	0.376522i	$-0.877120\pi$
$997$	−4.30387e6	+	7.45452e6i	−0.137126	+	0.237510i	0.789281	+	0.614032i	$0.210453\pi$
$998$	1.41806e7	+	2.45616e7i	0.450681	+	0.780603i
$999$	37834.7	−	359973.i	0.00119943	−	0.0114118i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	62.6.g.b.45.4	✓	56
31.20	even	15	inner	62.6.g.b.51.4	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
62.6.g.b.45.4	✓	56	1.1	even	1	trivial
62.6.g.b.51.4	yes	56	31.20	even	15	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 62 = 2 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	62.g (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.23607 + 3.80423i) q^{2} +(-0.311477 + 0.345930i) q^{3} +(-12.9443 - 9.40456i) q^{4} +(21.3689 - 37.0120i) q^{5} +(-0.930990 - 1.61252i) q^{6} +(-10.6596 + 101.419i) q^{7} +(51.7771 - 37.6183i) q^{8} +(25.3778 + 241.453i) q^{9} +(114.389 + 127.041i) q^{10} +(-518.211 + 230.722i) q^{11} +(7.28516 - 1.54851i) q^{12} +(-44.7808 - 9.51845i) q^{13} +(-372.647 - 165.913i) q^{14} +(6.14765 + 18.9205i) q^{15} +(79.1084 + 243.470i) q^{16} +(-530.921 - 236.381i) q^{17} +(-949.912 - 201.910i) q^{18} +(-1167.77 + 248.216i) q^{19} +(-624.686 + 278.128i) q^{20} +(-31.7638 - 35.2773i) q^{21} +(-237.176 - 2256.58i) q^{22} +(-1546.73 + 1123.76i) q^{23} +(-3.11408 + 29.6285i) q^{24} +(649.242 + 1124.52i) q^{25} +(91.5624 - 158.591i) q^{26} +(-182.943 - 132.916i) q^{27} +(1091.79 - 1212.55i) q^{28} +(-882.071 + 2714.74i) q^{29} -79.5768 q^{30} +(-5348.32 + 157.034i) q^{31} -1024.00 q^{32} +(81.5968 - 251.129i) q^{33} +(1555.50 - 1727.56i) q^{34} +(3525.95 + 2561.75i) q^{35} +(1942.27 - 3364.10i) q^{36} +(800.328 + 1386.21i) q^{37} +(499.167 - 4749.26i) q^{38} +(17.2409 - 12.5262i) q^{39} +(-285.908 - 2720.23i) q^{40} +(10156.5 + 11280.0i) q^{41} +(173.465 - 77.2316i) q^{42} +(12298.1 - 2614.04i) q^{43} +(8877.70 + 1887.01i) q^{44} +(9478.96 + 4220.30i) q^{45} +(-2363.19 - 7273.15i) q^{46} +(1481.36 + 4559.15i) q^{47} +(-108.864 - 48.4694i) q^{48} +(6267.44 + 1332.19i) q^{49} +(-5080.44 + 1079.88i) q^{50} +(247.141 - 110.034i) q^{51} +(490.138 + 544.353i) q^{52} +(-3923.82 - 37332.7i) q^{53} +(731.771 - 531.663i) q^{54} +(-2534.09 + 24110.3i) q^{55} +(3263.30 + 5652.20i) q^{56} +(277.866 - 481.279i) q^{57} +(-9237.17 - 6711.20i) q^{58} +(20419.8 - 22678.4i) q^{59} +(98.3623 - 302.728i) q^{60} -17662.2 q^{61} +(6013.49 - 20540.3i) q^{62} -24758.6 q^{63} +(1265.73 - 3895.53i) q^{64} +(-1309.21 + 1454.03i) q^{65} +(854.493 + 620.826i) q^{66} +(-29736.1 + 51504.5i) q^{67} +(4649.32 + 8052.87i) q^{68} +(93.0263 - 885.086i) q^{69} +(-14103.8 + 10247.0i) q^{70} +(-2131.56 - 20280.4i) q^{71} +(10397.0 + 11547.1i) q^{72} +(13120.4 - 5841.58i) q^{73} +(-6262.71 + 1331.18i) q^{74} +(-591.229 - 125.670i) q^{75} +(17450.2 + 7769.35i) q^{76} +(-17875.8 - 55016.1i) q^{77} +(26.3417 + 81.0715i) q^{78} +(19705.2 + 8773.34i) q^{79} +(10701.8 + 2274.73i) q^{80} +(-57604.2 + 12244.1i) q^{81} +(-55465.8 + 24694.9i) q^{82} +(3037.25 + 3373.21i) q^{83} +(79.3919 + 755.364i) q^{84} +(-20094.1 + 14599.2i) q^{85} +(-5256.88 + 50015.8i) q^{86} +(-664.364 - 1150.71i) q^{87} +(-18152.1 + 31440.3i) q^{88} +(-23274.6 - 16910.0i) q^{89} +(-27771.6 + 30843.5i) q^{90} +(1442.70 - 4440.18i) q^{91} +30589.8 q^{92} +(1611.55 - 1899.06i) q^{93} -19175.1 q^{94} +(-15766.9 + 48525.4i) q^{95} +(318.952 - 354.232i) q^{96} +(99907.2 + 72586.8i) q^{97} +(-12814.9 + 22196.1i) q^{98} +(-68859.7 - 119268. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 56 q^{2} - 7 q^{3} - 224 q^{4} + 91 q^{5} - 152 q^{6} - 94 q^{7} + 896 q^{8} + 896 q^{9} - 944 q^{10} - 31 q^{11} - 112 q^{12} - 1244 q^{13} + 856 q^{14} + 518 q^{15} - 3584 q^{16} + 1064 q^{17}+ \cdots - 625437 q^{99}+O(q^{100}) \) 56 * q + 56 * q^2 - 7 * q^3 - 224 * q^4 + 91 * q^5 - 152 * q^6 - 94 * q^7 + 896 * q^8 + 896 * q^9 - 944 * q^10 - 31 * q^11 - 112 * q^12 - 1244 * q^13 + 856 * q^14 + 518 * q^15 - 3584 * q^16 + 1064 * q^17 - 1724 * q^18 + 619 * q^19 - 1024 * q^20 + 9541 * q^21 + 124 * q^22 - 1717 * q^23 + 768 * q^24 - 24033 * q^25 - 1344 * q^26 + 22754 * q^27 + 1776 * q^28 + 11733 * q^29 + 13928 * q^30 + 57065 * q^31 - 57344 * q^32 - 11248 * q^33 - 10456 * q^34 - 7296 * q^35 - 42464 * q^36 - 1504 * q^37 - 29736 * q^38 - 19566 * q^39 + 4096 * q^40 + 35891 * q^41 + 40636 * q^42 + 66400 * q^43 + 23344 * q^44 - 27014 * q^45 - 7612 * q^46 + 36521 * q^47 - 3072 * q^48 + 121465 * q^49 - 13108 * q^50 - 236890 * q^51 - 19904 * q^52 - 143661 * q^53 - 91016 * q^54 + 106359 * q^55 + 5056 * q^56 + 13060 * q^57 + 59468 * q^58 + 230112 * q^59 + 8288 * q^60 - 49860 * q^61 + 26740 * q^62 + 66726 * q^63 - 57344 * q^64 + 201094 * q^65 - 30508 * q^66 + 74372 * q^67 - 4656 * q^68 - 599733 * q^69 + 29184 * q^70 + 23383 * q^71 - 27584 * q^72 - 66915 * q^73 + 186916 * q^74 + 553648 * q^75 - 152736 * q^76 + 120895 * q^77 + 142024 * q^78 - 452529 * q^79 - 50944 * q^80 - 365276 * q^81 - 14324 * q^82 - 469160 * q^83 - 50464 * q^84 - 127377 * q^85 + 215540 * q^86 + 217461 * q^87 + 39744 * q^88 - 155746 * q^89 + 820796 * q^90 - 142152 * q^91 - 5952 * q^92 + 342224 * q^93 + 29656 * q^94 + 756444 * q^95 + 7168 * q^96 + 325303 * q^97 + 533540 * q^98 - 625437 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more